# Conditions for Triangle Similarity

ID: fusoj-varon Illustrative Math
Subject: Geometry

# Conditions for Triangle Similarity

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##### Problem 1

1) What is the length of segment ﻿$DF$﻿? ##### Problem 2

2) In triangle ﻿$ABC$﻿, angle ﻿$A$﻿ is 35º and angle ﻿$B$﻿ is 20º. Select all triangles which are similar to triangle ﻿$ABC$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) Triangle ﻿$DEF$﻿ where angle ﻿$D$﻿ is ﻿$35\degree$﻿ and angle ﻿$E$﻿ is ﻿$20\degree$﻿.﻿$\quad$﻿b) Triangle ﻿$GHI$﻿ where angle ﻿$G$﻿ is ﻿$35\degree$﻿ and angle ﻿$I$﻿ is ﻿$30\degree$﻿.

c) Triangle ﻿$JKL$﻿ where angle ﻿$J$﻿ is ﻿$35\degree$﻿ and angle ﻿$L$﻿ is ﻿$125\degree$﻿.﻿$\quad$﻿d) Triangle ﻿$MNO$﻿ where angle ﻿$N$﻿ is ﻿$20\degree$﻿ and angle ﻿$O$﻿ is ﻿$125\degree$﻿.

e) Triangle ﻿$PQR$﻿ where angle ﻿$Q$﻿ is ﻿$20\degree$﻿ and angle ﻿$R$﻿ is ﻿$30\degree$﻿.

##### Problem 3 3) Are triangles ﻿$ABC$﻿ and ﻿$DEC$﻿ similar?

True or false? Write below.

4) Explain or show your reasoning.

##### Problem 4

5) Lin is trying to convince Andre that all circles are similar. Help her write a valid justification for why all circles are similar.

##### Problem 5 6) Must these parallelograms be similar?

True or false? Write below.

##### Problem 6

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

8) An equilateral triangle and a right triangle are similar.

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

9) A right triangle and an isosceles triangle are similar.

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

10) Explain or show your reasoning.

##### Problem 7

11) Quadrilaterals ﻿$Q$﻿ and ﻿$P$﻿ are similar. What is the scale factor of the dilation that takes ﻿$P$﻿ to ﻿$Q$﻿? a) $\frac{3}{5}$b) $\frac{4}{5}$c) $\frac{5}{4}$d) $\frac{5}{3}$
##### Problem 8

The circle centered at ﻿$Q$﻿ is a scaled copy of the circle centered at ﻿$R$﻿. 12) Find the scale factor.

13) Find the value of ﻿$x$﻿.