problem solving with similar figures worksheet

Similar Figures Worksheets

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other, and that's we will learn in similar figures worksheets. Similar figures have the same shape but different sizes. For example, two circles (of any radii) will always superimpose each other because they are similar. Similar figures worksheets help students understand the concept and importance of similar figures.

Benefits of Similar Figures Worksheets

When two figures have the same shape and size, they are congruent. If the figures have the same shape, but not the same size, they are similar. Solve the similar figure worksheets to explore more examples and problems. Real life examples include Front wheels of a car, hands of a person, heights of towers and trees and building architecture.

Download Similar Figures Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

Home » Worksheets » 9 Similar Figures Worksheets For Fun And Engaging Ways To Teach Geometry

9 Similar Figures Worksheets For Fun And Engaging Ways To Teach Geometry

If you’re in search of a top-quality collection of similar figures worksheets, your hunt is over! Teach Simple has gathered an extensive selection of professionally crafted resources to help students learn and practice working with similar figures.

Things to look for when choosing a similar figures worksheet

As a math teacher, it is essential that your students understand and demonstrate proficiency in similar figures. This knowledge will be indispensable when they progress through the rest of geometry and move onto more complex math concepts. After completing this lesson, you can feel confident that your pupils have mastered recognizing similar figure problems as well as know how to solve them independently.

To properly assess the students’ work, search for worksheets that have plenty of room to draw multiple triangles and show their computations. Depending on the complexity of the lesson, you may be able to grade these sheets without needing a separate answer key; however, answer keys are always helpful – especially if you have a sub or student grading.

9 best similar figures worksheets

• Digital Math For 5.G.4 – Classifying 2D Figures (Slides + Self-Grading Quiz) By Markers And Minions

To help students master the 5.G.4 standard, this resource includes slides in both PowerPoint and Google Slides formats that are interactive and engaging by having students drag, drop, and sort images to identify similar triangles visually. To assess student progress on a deeper level, there is also an included self-grading Google Forms quiz that can provide valuable data for teachers. The easy-to-assign Google Slides version makes it simple to use through Google Classroom!

• Real-World Shape Identification By Life Beyond The Gradebook

This is a five page packet of worksheets from Life Beyond the Gradebook to help kindergarten and first-grade students identify circles, triangles, and rectangles in every day objects.

• Color, Trace, And Connect Shapes From Math Worksheets 4 Kids

Get your preschoolers and kindergarteners excited about learning shapes with our shape-themed coloring, tracing, and drawing activities! Math Worksheets 4 Kids are designed to help kids explore each 2D shape in a fun way. From rectangles to circles to polygons – we have it all covered! In these worksheets your students will color, trace and draw these shapes: Rectangle, Square, Triangle, Circle Quadrilateral Polygon. This worksheet and answer key are free. Two others with similar problems are available for a fee.

•  Similar Figures Worksheet From Math Worksheets 4 Kids

Use this worksheet to enhance students ability on how to determine similar figures. Each page has an activity to determine the similar figure from the given figure. Also, learners will be tasked with constructing their own figures from the given triangle using the provided measurements. Finally, students will be encouraged to consider how this concept might apply in real life circumstances by answering a reflective question.

• Similar Figures Worksheets From CueMath

In this worksheet from CueMath, students are given the lengths of the sides of various shapes, then asked to determine if the shapes are similar. This is a good problem set for students in middle school . The worksheet and answer key are free, but they contain advertisements for tutoring from CueMath.

• 3D Shapes From Worksheet Zone

This is a clever worksheet to gives students practice identifying 3D shapes in common objects. Shapes include a cylinder, cone, cube, sphere. Ideally, this worksheet should be printed in color. It is free on the Worksheet Zone website and includes an answer key.

• Similar Figures Practice Worksheets From Kuta Software

Kuta Software Worksheets always has well-designed worksheets with plenty of white space and progressively more difficult problems! The similar figures worksheet contains only triangles.  But gives students practice identifying similarity by proportion. It’s a good fit for middle and high school students. This one is free and includes an answer sheet.

• Similar Shapes Worksheet From Cazoomy

You’ll need a paid subscription to access Cazoomy worksheets like this one. This is one of several worksheets where students can practice identifying shapes on a coordinate grid. The worksheets are designed for students in high school or late middle school.

• Match The Shapes Worksheet From Education.com

This guided lesson from Education.com is designed for preschoolers and kindergartners. It gives practice finding circles, triangles, squares, and rectangles in every day objects. One of the best pages in this packet is a cutout of a museum where students identify shapes in everyday (and some imaginative) objects. The worksheet and answer key is included in the teacher subscription plan.

As an educator, you can relate to the monotony of constantly assigning math worksheets from a textbook. That’s why so many teachers have decided to invest in materials that will spark creativity and engage their students! It may take effort for one to find quality algebra worksheets that fit their class, but once discovered they’ll save precious time both now and later on – making them truly worth every penny spent!

Trying to find a paid worksheet that is both teaching-appropriate and aesthetically pleasing can be tricky. You must buy the sheet without actually viewing it first, making this difficult for teachers targeting high school or adult students who may not appreciate ‘cute’ visuals. Thumbnails previews and obscured screenshots make it nearly impossible to accurately gauge how the material will appear before you invest your money.

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Here at Teach Simple, we strive to fuel your educational mission and provide the necessary tools needed for success. This list of similar figures worksheets is designed with that in mind: helping you! So, rest assured knowing that our resources are here to assist you every step of the way as they have been developed with care by educators just like yourself.

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Similar Shapes

Similar‌ ‌Shapes‌

Here‌ ‌we‌ ‌will‌ ‌learn‌ ‌about‌ ‌similar‌ ‌shapes‌ ‌in‌ ‌maths,‌ ‌including‌ ‌what‌ ‌they‌ ‌are‌ ‌and‌ ‌how‌ ‌to‌ ‌identify‌ ‌similar‌ ‌shapes.‌ ‌We‌ ‌will‌ ‌also‌ ‌solve‌ ‌problems‌ ‌involving‌ ‌similar‌ ‌shapes‌ ‌where‌ ‌the‌ ‌scale‌ ‌factor‌ ‌is‌ ‌known‌ ‌or‌ ‌can‌ ‌be‌ ‌found.‌ 

There‌ ‌are‌ ‌similar‌ ‌shapes‌ ‌worksheets‌ ‌based‌ ‌on‌ ‌Edexcel,‌ ‌AQA‌ ‌and‌ ‌OCR‌ ‌exam‌ ‌questions,‌ ‌along‌ ‌with‌ ‌further‌ ‌guidance‌ ‌on‌ ‌where‌ ‌to‌ ‌go‌ ‌next‌ ‌if‌ ‌you’re‌ ‌still‌ ‌stuck.‌

What are similar shapes?

Similar shapes are enlargements of each other using a scale factor.

All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio. 

These two rectangles are similar shapes. 

The scale factor of enlargement from shape A to shape B is 2 .

The angles are all 90^o

The ratio of the bases is 2:4 which simplifies to 1:2

The ratio of the heights is also 1:2

These two parallelograms are similar shapes.

The scale factor of enlargement from shape A to shape B is 3.

The corresponding angles are all equal, 45^o and 135^o .

The ratio of the bases are 3:9 which simplifies to 1:3

The ratio of the perpendicular heights is also 1:3

See also: Enlargement

Scale factor for length, area and volume

The scale factors for length, area and volume are not the same.

In Higher GCSE Maths similar shapes are extended to look at area scale factor and volume scale factors

To work out the length scale factor we divide the length of the enlarged shape by the length of the original shape.

To work the area scale factor we square the length scale factor.

To work the volume scale factor we cube the length scale factor.

• Comparing length A and length B we can work out the scale factor to be 3 .
• Comparing area A and area B we can work out the scale factor to be 9 . This is the same as 3^2 .
• Comparing volume A and volume B we can work out the scale factor to be 27 . This is the same as 3^3 .

Step-by-step guide: Scale factor

How to decide if shapes are similar

In order to decide if shapes are similar:

Decide which sides are pairs of corresponding sides.

Find the ratios of the sides.

Check if the ratios are the same.

Explain how to decide if shapes are similar

Similar shapes worksheet

Get your free similar shapes worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on congruence and similarity

Similar shapes  is part of our series of lessons to support revision on  congruence and similarity . You may find it helpful to start with the main congruence and similarity lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Congruence and similarity
• Congruent triangles
• Congruent shapes

Similar shapes examples

Example 1: decide if shapes are similar.

Are these shapes similar?

The bases of the rectangles are a pair of corresponding sides.

The heights of the rectangles are a pair of corresponding sides.

2 Find the ratios of the sides.

When writing the ratios the order is very important.

Here the ratio is length A : length B

The ratio of the bases is 1:2

The ratio of the heights is 2:4 which simplifies to 1:2

3 Check if the ratios are the same.

The rectangles are similar shapes. The ratios for the corresponding lengths are the same 1:2.  

The scale factor of enlargement for shape A to shape B is 2 .

Example 2: decide if shapes are similar

The bases of the triangles are a pair of corresponding sides.

The heights of the triangles are a pair of corresponding sides.

The ratio of the heights is 5:15 which simplifies to 1:3

The ratio of the bases is 7:20 this can be written as 1: \frac{20}{7} or 1:2.857...

The triangles are NOT similar shapes. The ratios for the corresponding lengths are NOT the same.

How to find a missing length

In order to find a missing side in a pair of similar shapes:

Find the scale factor.

Use the scale factor to find the missing length.

Missing length examples

Example 3: finding a missing length.

Here are two similar shapes. Find the length QR.

Pair up the sides that have measurements. Make sure you pair up the side mentioned in the question.

The sides AB and PQ are a pair of corresponding sides.

The sides BC and QR are a pair of corresponding sides.

The ratio of the lengths AB : PQ is 9:27 which simplifies to 1:3

This gives a scale factor of enlargement from rectangle ABCD to rectangle PQRS of 3.

The ratio of the lengths BC : QR is also 1:3

We can use the scale factor 3 as a multiplier to find the missing length.

The missing side has been found.  QR = 12 cm

Alternatively an equation may be formed and solved:

Example 4: finding a missing length

Here are two similar triangles. Find the length BC.

Pair up the sides that have measurements. Make sure you pair up the side mentioned in the question. Use the angles to help you.

The sides AB and DE are a pair of corresponding sides.

The sides BC and EF are a pair of corresponding sides.

The ratio of the lengths AB : DE is 12.5 : 25 which simplifies to 1 : 2

This gives a scale factor of enlargement from triangle ABC to triangle DEF of 2.

But we want a scale factor from DEF to ABC which will be \frac{1}{2} .

The ratio of the lengths BC : EF is also 1:2

We can use the scale factor \frac{1}{2} as a multiplier to find the missing length.

18\times\frac{1}{2}=9

The missing side has been found.  BC = 9 \; cm

How to find a missing length in a triangle

In order to find a missing side in a pair of triangles when you are not told that the triangles are similar:

Use angle facts to determine which angles are equal.

Redraw the triangles side by side.

Missing length in a triangle examples

Example 5: finding a missing length in a triangle.

Work out the value of x.

Look for equal angles.

angle ACB = angle DCE as vertically opposite angles are equal

There are a pair of parallel sides – AB and DE.  This means that there are equal angles as there are alternate angles.

Angle ABC = angle CED (alternate angles)

Angle BAC = angle CDE (alternate angles)

It makes the problem much easier if you redraw the triangles side-by-side so that it is easier to pair up the corresponding sides.

The sides AC and DC are a pair of corresponding sides.

The sides BC and EC are a pair of corresponding sides.

The ratio of the lengths AC : DC is 4 : 10 which simplifies to 1 : 2.5

This gives a scale factor of enlargement from ABC to CDE of 2.5

The ratio of the lengths BC : EC is also 1 : 2.5

We can use the scale factor 2.5 as a multiplier to find the missing length.

x=5 \times 2.5=12.5

The value of x has been found, x=12.5

Example 6: finding a missing length in a triangle

angle EAB = angle DAC as they are common to both triangles

There are a pair of parallel sides – EB and DC.  This means that there are equal angles as there are corresponding angles.

angle AEB = angle ADC (corresponding angles)

angle ABE = angle ACD (corresponding angles)

Pair up the sides that have measurements.  Make sure you pair up the side mentioned in the question.  Use the angles to help you.

The sides AE and AD are a pair of corresponding sides.

The sides EB and DC are a pair of corresponding sides.

The ratio of the lengths AE : AD is 5 : 8 which simplifies to 1 : \frac{8}{5} or 1 : 1.6

This gives a scale factor of enlargement from ABE to ACD of 1.6

The ratio of the lengths EB : DC is also 1 : 1.6

We can use the scale factor 1.6 as a multiplier to find the missing length.

x=7 \times 1.6=11.2

The value of x has been found, x=11.2

How to find an area or volume using similar shapes

In order to find an area or volume using similar shapes:

Use the scale factor to find the missing value.

Area or volume using similar shapes examples

Example 7: finding an area or volume.

These two figures are similar.

The area of shape A is 60 \; cm^2 . 

Find the area of shape B:

Use the given information to write a ratio and work out the scale factor.

When writing the ratios the order is very important. 

\begin{aligned} \text{The ratio of the lengths is} \ \text{length} \; A&: \text{length} \; B\\\\ 5&:10\\\\ \text{which simplifies to} \quad 1&:2 \end{aligned}

The scale factor of enlargement from shape A to shape B is 2

As we are finding an area we need to square the ratio of the lengths, and square the scale factor.

\begin{aligned} \text{The ratio of the lengths is -} \ \text{length} \ A&:\text{length} B\\\\ 1&:2\\\\ \text{The ratio of the areas is -} \ \text{area} \ A&:\text{area} \ B\\\\ 1^2&:2^2\\\\ \text{which simplifies to -}\ \ \ \ \ \ 1&:4 \end{aligned}

We can use the area scale factor 2^2 or 4 as a multiplier to find the missing area.

60\times 4=240

The area of shape B is 240 \; cm^2

Alternatively you can form an equation to solve:

Example 8: finding an area or volume

These two shapes are similar. 

The volume of shape A is 400 \; cm^3 . 

Find the volume of shape B:

​ \begin{aligned} \text{The ratio of the lengths is} \ \text{length } A&: \text{length } B\\\\ 10&:15\\\\ \text{which simplifies to} \quad 1&:1.5 \end{aligned}

The scale factor of enlargement from shape A to shape B is 1.5

As we are finding a volume we need to cube the ratio of the lengths, and cube the scale factor.

\begin{aligned} \text{The ratio of the lengths is -} \ \text{length} \ A&:\text{length} B\\\\ 1&:1.5\\\\ \text{The ratio of the volumes is -} \ \text{volume} \ A&:\text{volume} \ B\\\\ 1^3&:1.5^3\\\\ \text{which simplifies to -}\ \ \ \ \ \ 1&:3.375 \end{aligned}

We can use the volume scale factor 1.5^3 or 3.375 as a multiplier to find the missing volume.

400\times 3.375=1350

The volume of shape B is 1350 \; cm^3

Common misconceptions

• Take care with the order of ratios

Make sure that you are consistent with your ratios. E.g. In this example, always write the A value first, and then the B value. 1 : 3 and 2 : 6.   The ratios are equal, so these shapes are similar shapes.

• In most diagrams the diagrams are NOT drawn to scale

Often diagrams for questions involving similar shapes are NOT drawn to scale. So, use the measurements given, rather than measuring for yourself.

• Shapes can be similar but in different orientations

The second shape may be in a different orientation to the first shape. The shapes can still be similar. 

E.g. Here shape A and Shape B are similar.  Shape B is an enlargement of shape A by scale factor 2.

Here shape B has been rotated to make the similarity easier to see.

• Scaling up or down

If you are finding a missing length in the larger shape you can multiply by the scale factor.  The scale factor will be a number greater than 1 . If you are finding a missing length in the smaller shape you can multiply by the scale factor, but the scale factor will be a number between 0 and 1.

Practice similar shapes questions

1. Consider if these shapes are similar:

Yes – sides in ratio 1:4

No – sides in ratio 1:3 and 1:4

No – sides in ratio 1:3 and 1:2

Yes – sides in ratio 1:3

The shapes are similar as the ratio of the corresponding sides are the same.

The ratio of the bases is \;\; 3:9 which simplifies to \quad \quad \;\; 1:3 the ratio of the heights is \; 1:3

2. Consider if these shapes are similar:

Yes – sides in ratio 2:1

Yes – sides in ratio 3:1

No – sides in ratio 2:1 and 1:2

No – sides in ratio 3:1 and 2:1

The ratio of the short sides is \;\; 4:2 which simplifies to \quad \quad \quad \quad \;2:1 the ratio of the long sides is \quad 8:4 which simplifies to \quad \quad \quad \quad \;2:1

3. These shapes are similar. Find the value of x.

The ratio of the bases is \;\; 6:12 which simplifies to \quad \quad \;\,1:2

The scale factor of enlargement is 2

4. These shapes are similar. Find the value of x.

The ratio of the bases is \;\; 6:9 which simplifies to \quad \quad \;\,1:\frac{9}{6} or \quad \quad \quad \quad \quad \quad \quad \quad \;\;1:1.5

The scale factor of enlargement is 1.5

5. Find the value of x.

Use the parallel lines to identify equal angles.  

Then we can find pairs of corresponding sides.

The ratio of the corresponding sides is \;\; 4:12 which simplifies to \quad \quad \quad \quad \quad \quad \quad \;\;\; 1:3

The scale factor of enlargement is \; 3

6. Find the value of x.

Use the parallel lines to identify equal angles.   

The ratio of the corresponding sides is \;\; 9:6 which simplifies to \quad \quad \quad \quad \quad \quad \quad \;\;\; 1:\frac{2}{3}

The scale factor of enlargement is \; \frac{2}{3}

Similar shapes GCSE questions

1. Which shape is similar to shape X?

2. Triangles ABC and DEF are similar.

(a)  Write down the size of angle y

(b)  Work out the value of x

x:11=4:8 the scale factor is \frac{1}{2}

ABC and AED are straight lines. BE is parallel to CD.

AD = 10.5 \;cm AE = 7.5 \; cm BE = 6.8 \; cm

Work out the length CD

Learning checklist

You have now learned how to:

• Compare lengths using ratio notation and/or scale factors
• Solve problems with similar shapes using ratio notation and/or scale factors
• Solve problem with areas and volumes using ratio notation and/or scale factors (HIGHER)

The next lessons are

• Transformations
• Loci and construction

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Unit 12: Similarity

About this unit.

Learn what it means for two figures to be similar, and how to determine whether two figures are similar or not. Use this concept to prove geometric theorems and solve some problems with polygons.

Definitions of similarity

• Similar shapes & transformations (Opens a modal)
• Similarity & transformations 4 questions Practice

Introduction to triangle similarity

• Intro to triangle similarity (Opens a modal)
• Triangle similarity postulates/criteria (Opens a modal)
• Determining similar triangles (Opens a modal)
• Proving slope is constant using similarity (Opens a modal)
• Triangle similarity review (Opens a modal)
• Determine similar triangles: Angles 4 questions Practice
• Determine similar triangles: SSS 4 questions Practice

Solving similar triangles

• Solving similar triangles (Opens a modal)
• Solving similar triangles: same side plays different roles (Opens a modal)
• Solve similar triangles (basic) 4 questions Practice
• Solve similar triangles (advanced) 4 questions Practice

Angle bisector theorem

• Intro to angle bisector theorem (Opens a modal)
• Using the angle bisector theorem (Opens a modal)
• Solve triangles: angle bisector theorem 4 questions Practice

Solving problems with similar and congruent triangles

• Using similar & congruent triangles (Opens a modal)
• Challenging similarity problem (Opens a modal)
• Use similar triangles 4 questions Practice

Solving modeling problems with similar and congruent triangles

• Geometry word problem: the golden ratio (Opens a modal)
• Geometry word problem: Earth & Moon radii (Opens a modal)
• Geometry word problem: a perfect pool shot (Opens a modal)

Similar Shapes Sides Practice Questions

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Similar and Congruent Figures

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8.7: Solve Proportion and Similar Figure Applications

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• Page ID 15179

Learning Objectives

By the end of this section, you will be able to:

• Solve proportions
• Solve similar figure applications

Before you get started, take this readiness quiz.

If you miss a problem, go back to the section listed and review the material.

• Solve \(\dfrac{n}{3}=30\). If you missed this problem, review Exercise 2.2.25 .
• The perimeter of a triangular window is 23 feet. The lengths of two sides are ten feet and six feet. How long is the third side? If you missed this problem, review Example 3.4.2

Solve Proportions

When two rational expressions are equal, the equation relating them is called a proportion .

Definition: PROPORTION

A proportion is an equation of the form \(\dfrac{a}{b}=\dfrac{c}{d}\), where \(b \ne 0\), \(d \ne 0\).

The proportion is read “a is to b, as c is to d"

The equation \(\dfrac{1}{2}=\dfrac{4}{8}\) is a proportion because the two fractions are equal.

The proportion \(\dfrac{1}{2}=\dfrac{4}{8}\) is read “1 is to 2 as 4 is to 8.”

Proportions are used in many applications to ‘scale up’ quantities. We’ll start with a very simple example so you can see how proportions work. Even if you can figure out the answer to the example right away, make sure you also learn to solve it using proportions.

Suppose a school principal wants to have 1 teacher for 20 students. She could use proportions to find the number of teachers for 60 students. We let x be the number of teachers for 60 students and then set up the proportion:

\[\dfrac{1\,\text{teacher}}{20\,\text{students}}=\dfrac{x\,\text{teachers}}{60\,\text{students}}\nonumber\]

We are careful to match the units of the numerators and the units of the denominators—teachers in the numerators, students in the denominators.

Since a proportion is an equation with rational expressions, we will solve proportions the same way we solved equations in Solve Rational Equations . We’ll multiply both sides of the equation by the LCD to clear the fractions and then solve the resulting equation.

Now we’ll do a few examples of solving numerical proportions without any units. Then we will solve applications using proportions.

Example \(\PageIndex{1}\)

\(\dfrac{x}{63}=\dfrac{4}{7}\).

Try It \(\PageIndex{1}\)

\(\dfrac{n}{84}=\dfrac{11}{12}\).

Try It \(\PageIndex{2}\)

\(\dfrac{y}{96}=\dfrac{13}{12}\).

Example \(\PageIndex{2}\)

\(\dfrac{144}{a}=\dfrac{9}{4}\).

Try It \(\PageIndex{3}\)

\(\dfrac{91}{b}=\dfrac{7}{5}\).

Try It \(\PageIndex{4}\)

\(\dfrac{39}{c}=\dfrac{13}{8}\).

Example \(\PageIndex{3}\)

\(\dfrac{n}{n+14}=\dfrac{5}{7}.\)

Try It \(\PageIndex{5}\)

\(\dfrac{y}{y+55}=\dfrac{3}{8}\).

Try It \(\PageIndex{6}\)

\(\dfrac{z}{z−84}=−\dfrac{1}{5}\).

Example \(\PageIndex{4}\)

\(\dfrac{p+12}{9}=\dfrac{p−12}{6}\).

Try It \(\PageIndex{7}\)

\(\dfrac{v+30}{8}=\dfrac{v+66}{12}\).

Try It \(\PageIndex{8}\)

\(\dfrac{2x+15}{9}=\dfrac{7x+3}{15}\).

To solve applications with proportions, we will follow our usual strategy for solving applications. But when we set up the proportion, we must make sure to have the units correct—the units in the numerators must match and the units in the denominators must match.

Example \(\PageIndex{5}\)

When pediatricians prescribe acetaminophen to children, they prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of the child’s weight. If Zoe weighs 80 pounds, how many milliliters of acetaminophen will her doctor prescribe?

Try It \(\PageIndex{9}\)

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?

Try It \(\PageIndex{10}\)

For every 1 kilogram (kg) of a child’s weight, pediatricians prescribe 15 milligrams (mg) of a fever reducer. If Isabella weighs 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe?

Example \(\PageIndex{6}\)

A 16-ounce iced caramel macchiato has 230 calories. How many calories are there in a 24-ounce iced caramel macchiato?

Try It \(\PageIndex{11}\)

At a fast-food restaurant, a 22-ounce chocolate shake has 850 calories. How many calories are in their 12-ounce chocolate shake? Round your answer to nearest whole number.

464 calories

Try It \(\PageIndex{12}\)

Yaneli loves Starburst candies, but wants to keep her snacks to 100 calories. If the candies have 160 calories for 8 pieces, how many pieces can she have in her snack?

Example \(\PageIndex{7}\)

Josiah went to Mexico for spring break and changed $325 dollars into Mexican pesos. At that time, the exchange rate had $1 US is equal to 12.54 Mexican pesos. How many Mexican pesos did he get for his trip?

Try It \(\PageIndex{13}\)

Yurianna is going to Europe and wants to change $800 dollars into Euros. At the current exchange rate, $1 US is equal to 0.738 Euro. How many Euros will she have for her trip?

590.4 Euros

Try It \(\PageIndex{14}\)

Corey and Nicole are traveling to Japan and need to exchange $600 into Japanese yen. If each dollar is 94.1 yen, how many yen will they get?

In the example above, we related the number of pesos to the number of dollars by using a proportion. We could say the number of pesos is proportional to the number of dollars. If two quantities are related by a proportion, we say that they are proportional.

Solve Similar Figure Applications

When you shrink or enlarge a photo on a phone or tablet, figure out a distance on a map, or use a pattern to build a bookcase or sew a dress, you are working with similar figures . If two figures have exactly the same shape, but different sizes, they are said to be similar. One is a scale model of the other. All their corresponding angles have the same measures and their corresponding sides are in the same ratio.

Definition: SIMILAR FIGURES

Two figures are similar if the measures of their corresponding angles are equal and their corresponding sides are in the same ratio.

For example, the two triangles in Figure are similar. Each side of ΔABC is 4 times the length of the corresponding side of ΔXYZ.

This is summed up in the Property of Similar Triangles.

Definition: PROPERTY OF SIMILAR TRIANGLES

• If ΔABC is similar to ΔXYZ

To solve applications with similar figures we will follow the Problem-Solving Strategy for Geometry Applications we used earlier.

Definition: SOLVE GEOMETRY APPLICATIONS.

• Read the problem and make all the words and ideas are understood. Draw the figure and label it with the given information.
• Identify what we are looking for.
• Name what we are looking for by choosing a variable to represent it.
• Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
• Solve the equation using good algebra techniques.
• Check the answer in the problem and make sure it makes sense.
• Answer the question with a complete sentence.

Example \(\PageIndex{8}\)

ΔABC is similar to ΔXYZ. The lengths of two sides of each triangle are given in the figure.

Find the length of the sides of the similar triangles.

Try It \(\PageIndex{15}\)

ΔABC is similar to ΔXYZ. The lengths of two sides of each triangle are given in the figure.

Find the length of side a

Try It \(\PageIndex{16}\)

The next example shows how similar triangles are used with maps.

Example \(\PageIndex{9}\)

On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in the figure below. If the actual distance from Los Angeles to Las Vegas is 270 miles find the distance from Los Angeles to San Francisco.

Try It \(\PageIndex{17}\)

On the map, Seattle, Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.

Try It \(\PageIndex{18}\)

Using the map above, find the distance from Portland to Boise.

We can use similar figures to find heights that we cannot directly measure.

Example \(\PageIndex{10}\)

Tyler is 6 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a tree was 24 feet long. Find the height of the tree.

Try It \(\PageIndex{19}\)

A telephone pole casts a shadow that is 50 feet long. Nearby, an 8 foot tall traffic sign casts a shadow that is 10 feet long. How tall is the telephone pole?

Try It \(\PageIndex{20}\)

A pine tree casts a shadow of 80 feet next to a 30-foot tall building which casts a 40 feet shadow. How tall is the pine tree?

Key Concepts

• Read the problem and make sure all the words and ideas are understood. Draw the figure and label it with the given information.

Free Printable Similar Figures Worksheets for 7th Grade

Math: Discover an extensive collection of free printable Similar Figures worksheets tailored for Grade 7 students and teachers. Enhance learning and explore the world of geometry with Quizizz.

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Explore printable Similar Figures worksheets for 7th Grade

Similar Figures worksheets for Grade 7 are an essential tool for teachers looking to enhance their students' understanding of Math and Geometry concepts. These worksheets provide a variety of problems and exercises that challenge students to identify, compare, and analyze similar figures in different contexts. By incorporating these worksheets into their lesson plans, teachers can effectively reinforce key concepts such as ratios, proportions, and scale factors, while also encouraging critical thinking and problem-solving skills. Furthermore, these worksheets are designed to align with Grade 7 curriculum standards, ensuring that students are well-prepared for more advanced Math and Geometry topics in the future.

Quizizz is an excellent platform that not only offers Similar Figures worksheets for Grade 7 but also provides a wide range of additional resources for teachers to utilize in their classrooms. With Quizizz, educators can access a vast library of interactive quizzes, games, and activities that cover various Math and Geometry topics, making it an invaluable tool for engaging students and reinforcing learning. The platform also allows teachers to track student progress and performance, enabling them to identify areas where students may need additional support or practice. By incorporating Quizizz into their teaching strategies, educators can create a dynamic and interactive learning environment that fosters a deeper understanding of Math and Geometry concepts for Grade 7 students.

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Similar Figures Word Problems

Similar Figures Word Problems - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Similar figure word problems, Solving proportion word problems involving similar figures, Proportions, Similar figures 61b, Chapter 7 similar figures, Proportions and similar figures, Similar triangles word problems, Word problem practice workbook.

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1. Similar Figure Word Problems -

2. solving proportion word problems involving similar figures, 3. proportions, 4. similar figures 61b, 5. chapter 7: similar figures, 6. proportions and similar figures -, 7. similar triangles word problems, 8. word problem practice workbook.