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Similar Triangles

Understand similarity to calculate lengths in rotated and reflected triangles.
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This is level 3: Questions without diagrams. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

1

Triangle ABC is similar to triangle DEF. The corresponding vertices are A and D, B and E, C and F. Which side corresponds to AB?

Match the letters in the same positions: A matches D and B matches E.

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2

Triangle ABC is similar to triangle PQR. Side AB corresponds to side PQ. If AB = 5 cm and PQ = 15 cm, find the scale factor from triangle ABC to triangle PQR.

Divide the length in the larger triangle by the matching length in the smaller triangle.

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3

Triangle ABC is similar to triangle DEF. Side AB corresponds to side DE and side AC corresponds to side DF. If AB = 6 cm, DE = 18 cm and AC = 8 cm, find DF.

First find the scale factor from AB to DE, then multiply AC by that scale factor.

☐ cm ☐ ✓ ✗

4

Two similar triangles have corresponding sides 4 cm and 14 cm. Another pair of corresponding sides is 6 cm and x cm where x is greater than 6. Find x.

Use the first pair of sides to find the scale factor, then apply it to 6 cm.

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5

Triangle JKL is similar to triangle RST. Side JK corresponds to RS and side KL corresponds to ST. If JK = 9 cm, RS = 6 cm and KL = 15 cm, find ST.

This is a reduction, so the scale factor is less than 1. Compare RS with JK.

☐ cm ☐ ✓ ✗

6

Two similar triangles have corresponding side lengths of 5 cm and 20 cm. Another side in the smaller triangle is 6 cm. Find the corresponding side in the larger triangle.

Find the scale factor using 5 cm and 20 cm, then multiply 6 cm by that scale factor.

☐ cm ☐ ✓ ✗

7

Two similar triangles have corresponding side lengths of 18 cm and 12 cm. Another side in the larger triangle is 21 cm. Find the corresponding side in the smaller triangle.

Compare the smaller triangle with the larger triangle. You may need to divide rather than multiply.

☐ cm ☐ ✓ ✗

8

In triangle ABC, point D lies on AB and point E lies on AC. DE is parallel to BC. AD = 6 cm, DB = 4 cm and AE = 9 cm. Find EC.

Triangles ADE and ABC are similar. First find AB, then compare AD with AB.

☐ cm ☐ ✓ ✗

9

In triangle PQR, point S lies on PQ and point T lies on PR. ST is parallel to QR. PS = 8 cm, SQ = 12 cm and PT = 10 cm. Find TR.

Triangles PST and PQR are similar. First find PQ, then use the same fraction on PR.

☐ cm ☐ ✓ ✗

10

Two similar triangles have perimeters 35 cm and 56 cm. A side of the smaller triangle is 15 cm. Find the corresponding side of the larger triangle.

For similar triangles, the perimeter scale factor is the same as the length scale factor.

☐ cm ☐ ✓ ✗

11

Triangle ABC has angles A = 42°, B = 58° and C = 80°. Triangle PQR has angles P = 58°, Q = 80° and R = 42°. Side AC = 12 cm and side RQ = 18 cm. If AB = 9 cm, find RP.

Use the equal angles to match the triangles correctly. AC corresponds to RQ, so use those sides to find the scale factor.

☐ cm ☐ ✓ ✗

12

Two line segments are labeled AB and CD. They intersect at E. Angles ACE and BDE are both 41 degrees. AE is equal to x cm and BE is equal to 3x cm. Find DC if EC is 17 mm.

☐ mm ☐ ✓ ✗

Check

Can you correct your mistakes in order to get full marks?

This is Similar Triangles level 3. You can also try:
Level 1 Level 2

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
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Description of Levels

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Level 0 - Match the pairs of similar triangles

Level 1 - Basic questions about similar triangles

Level 2 - Questions about overlapping triangles

Level 3 - Questions without diagrams

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Similar Parts Puzzle - Use the colours to dissect the outlines into similar parts.

Similar Shapes - Area factor and Volume factor.

More on Enlargements including lesson Starters, visual aids, investigations and self-marking exercises.

Square in Rectangle - An advanced lesson Starter.

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Similar Shapes

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Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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