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• Printable Similar Triangles Worksheets in PDF: Practice Proportions and Diagrams

Printable Similar Triangles Worksheets in PDF: Practice Proportions and Diagrams

These free printable similar triangles worksheets give grade 7 students practice identifying similar triangles and setting up proportions between their corresponding sides. Each worksheet is a downloadable PDF that includes an answer key, so students can check their own work.

Problems include comparing equilateral and isosceles triangles, along with word problems that connect triangle similarity to real-life fields like architecture and engineering. For more Grade 7 practice, explore Brighterly’s geometry worksheets hub.

Similar Triangles Worksheets: Free Download

This topic is available as four downloadable worksheet files:

What Makes Two Triangles Similar

Two triangles are similar when they have the same ratio of corresponding sides and equal pairs of corresponding angles. This means the triangles have the same shape, even if their size is different — one triangle is essentially a scaled-up or scaled-down version of the other.

Setting Up a Proportion Between Similar Triangles

Once two triangles are confirmed similar, their corresponding sides all share the same scale factor. Setting up a proportion means writing each pair of matching sides as equal fractions, then using that relationship to compare or solve for an unknown length.

Triangle ABC has sides 6, 8, and 10. Triangle DEF has sides 12, 16, and 20.

• 6 ÷ 12 = 0.5
• 8 ÷ 16 = 0.5
• 10 ÷ 20 = 0.5

Every pair of corresponding sides reduces to the same ratio, 1:2, which confirms the triangles are similar and shows that Triangle DEF is twice the size of Triangle ABC.

Worked Example: Finding a Missing Side

Triangle GHI is similar to Triangle JKL. Side GH = 5 and its corresponding side JK = 15, so the scale factor from GHI to JKL is 3. Side HI = 7. Find the length of side KL.

• Set up the proportion: 5/15 = 7/x
• Cross multiply: 5x = 15 × 7
• Solve: 5x = 105, so x = 21

KL = 21

More Geometry Worksheets

Once your child is confident with similar triangles, explore more of Brighterly’s geometry practice:

• Triangle Congruence Worksheets
• Classifying Triangles Worksheets
• Types of Triangles Worksheets
• Missing Angles in Triangles Worksheets
• Scale Factor Worksheets
• Special Right Triangles Worksheets
• Area of a Triangle Worksheets

What Kids Practice With These Similar Triangles Worksheets

• Identifying similar triangles using equal angles and proportional sides
• Setting up and solving proportions between corresponding sides
• Comparing equilateral and isosceles triangles
• Solving word problems that apply triangle similarity to real-life situations
• Checking work against an included answer key

Each worksheet includes an answer key, so students can check their own results without waiting for a teacher to grade the page. Working through labeled diagrams and proportion setups helps students see similarity as a relationship between sides and angles, not just a definition to memorize.

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FAQ

What does it mean for two triangles to be similar?

Two triangles are similar when their corresponding angles are equal, and their corresponding sides share the same ratio. This means the triangles have the same shape but not necessarily the same size — one is a scaled version of the other. Similarity is different from congruence, where the triangles must also be the same size.

What grade are these similar triangles worksheets for?

This set of similar triangles worksheets is written for grade 7 students who are building on earlier geometry skills like identifying triangle types and working with ratios. Problems include comparing equilateral and isosceles triangles and setting up proportions, matching the level where most seventh graders study triangle similarity in class.

How do you set up a proportion between similar triangles?

Write each pair of corresponding sides as a fraction, with the same triangle’s side in the same position in both fractions, then set the fractions equal to each other. If one side length is unknown, cross-multiply the proportion and solve for that value, the same way you would solve any equation with a fraction on each side.

Do these worksheets include an answer key?

Yes, each similar triangles worksheet in this set comes with an answer key. Students can check their own results as soon as they finish a page, which helps them catch mistakes in a proportion setup or a cross-multiplication step right away, instead of waiting for a teacher to grade the assignment.

Are these similar triangles worksheets free and printable?

Yes, every worksheet in this set is free to download as a printable PDF, and no account or sign-up is required. Families can print the pages for hands-on practice with a pencil and ruler, or complete the problems digitally if a printer isn’t available, since the questions work equally well either way.