# Conditions for Triangle Similarity

13 questions

# Conditions for Triangle Similarity

##### 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 $\textbf{all}$ 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?

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?

7) Explain your reasoning.

##### 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.

Must be true

Could be true

Cannot be true

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

Must be true

Could be true

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 $Q$?

$\frac{3}{5}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{5}{3}$

##### 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 $x$.