Other Conditions for Triangle Similarity

ID: daras-riruv
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Other Conditions for Triangle Similarity

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Problem 1


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1) Explain how we know that triangle ABCABC and triangle DEFDEF are similar.

2) What does that tell us about angle DD?

Problem 2


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3) Find the length of EFEF.

4) Find the measure of angle EE.

5) Find the measure of angle FF.

Problem 3


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6) Are triangles ABCABC and DECDEC similar?

True or false? Write below.

7) Explain your reasoning.

Problem 4

8) What is the length of segment DFDF?

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a) 3 units\text{3 units}b) 814 units \frac{81}{4} \text{ units}c) 36 units\text{36 units}d) 48 units\text{48 units}
Problem 5

9) In triangle ABCABC, angle AA is 75º and angle BB is 20º. Select the triangle that is similar to triangle ABCABC.

a) Triangle DEF where angle D is 75° and angle E is 20°\text{Triangle } DEF \text{ where angle } D \text{ is } 75\degree \text{ and angle } E \text{ is } 20\degree b) Triangle DEF where angle D is 20° and angle E is 75°\text{Triangle } DEF \text{ where angle } D \text{ is } 20\degree \text{ and angle } E \text{ is } 75\degree c) Triangle DEF where angle D is 85° and angle E is 20°\text{Triangle } DEF \text{ where angle } D \text{ is } 85\degree \text{ and angle } E \text{ is } 20\degree d) Triangle DEF where angle D is 20° and angle E is 85°\text{Triangle } DEF \text{ where angle } D \text{ is } 20\degree \text{ and angle } E \text{ is } 85\degree
Problem 6

10) Sketch a pair of rectangles that are similar.

Problem 7

Determine if each statement must be true, could possibly be true, or definitely can't be true.

11) Two line segments are similar.

a) Must be true\text{Must be true}b) Could be true\text{Could be true}c) Cannot be true\text{Cannot be true}

12) Two angles are similar.

a) Must be true\text{Must be true}b) Could be true\text{Could be true}c) Cannot be true\text{Cannot be true}

13) Explain or show your reasoning.

Problem 8

Figure GG is the image of Figure GG' by a dilation.

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14) Where is the center of this dilation?

15) Estimate the scale factor.