# Other Conditions for Triangle Similarity

ID: daras-riruv
Illustrative Math
Subject: Geometry

# Other Conditions for Triangle Similarity

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##### Problem 1

1) Explain how we know that triangle ﻿$ABC$﻿ and triangle ﻿$DEF$﻿ are similar.

2) What does that tell us about angle ﻿$D$﻿?

##### Problem 2

3) Find the length of ﻿$EF$﻿.

4) Find the measure of angle ﻿$E$﻿.

5) Find the measure of angle ﻿$F$﻿.

##### Problem 3

6) Are triangles ﻿$ABC$﻿ and ﻿$DEC$﻿ similar?

True or false? Write below.

##### Problem 4

8) What is the length of segment ﻿$DF$﻿?

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

9) In triangle ﻿$ABC$﻿, angle ﻿$A$﻿ is 75º and angle ﻿$B$﻿ is 20º. Select the triangle that is similar to triangle ﻿$ABC$﻿.

a) $\text{Triangle } DEF \text{ where angle } D \text{ is } 75\degree \text{ and angle } E \text{ is } 20\degree$b) $\text{Triangle } DEF \text{ where angle } D \text{ is } 20\degree \text{ and angle } E \text{ is } 75\degree$c) $\text{Triangle } DEF \text{ where angle } D \text{ is } 85\degree \text{ and angle } E \text{ is } 20\degree$d) $\text{Triangle } DEF \text{ where angle } D \text{ is } 20\degree \text{ and angle } E \text{ is } 85\degree$
##### 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) $\text{Must be true}$b) $\text{Could be true}$c) $\text{Cannot be true}$

12) Two angles are similar.

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

13) Explain or show your reasoning.

##### Problem 8

Figure ﻿$G$﻿ is the image of Figure ﻿$G'$﻿ by a dilation.

14) Where is the center of this dilation?

15) Estimate the scale factor.