# Lesson 9

Conditions for Triangle Similarity

- Let’s prove some triangles similar.

### Problem 1

What is the length of segment \(DF\)?

### Problem 2

In triangle \(ABC\), angle \(A\) is 35º and angle \(B\) is 20º. Select **all** triangles which are similar to triangle \(ABC\).

triangle \(DEF\) where angle \(D\) is 35º and angle \(E\) is 20º

triangle \(GHI\) where angle \(G\) is 35º and angle \(I\) is 30º

triangle \(JKL\) where angle \(J\) is 35º and angle \(L\) is 125º

triangle \(MNO\) where angle \(N\) is 20º and angle \(O\) is 125º

triangle \(PQR\) where angle \(Q\) is 20º and angle \(R\) is 30º

### Problem 3

Decide whether triangles \(ABC\) and \(DEC\) are similar. Explain or show your reasoning.

### Problem 4

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

Must these parallelograms be similar? Explain your reasoning.

### Problem 6

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

- An equilateral triangle and a right triangle are similar.
- A right triangle and an isosceles triangle are similar.

### Problem 7

Quadrilaterals \(Q\) and \(P\) are similar.

What is the scale factor of the dilation that takes \(P\) to \(Q\)?

\(\frac35\)

\(\frac45\)

\(\frac54\)

\(\frac53\)

### Problem 8

The circle centered at \(Q\) is a scaled copy of the circle centered at \(R\).

- Find the scale factor.
- Find the value of \(x\).