Geometry | Unit 3 | Lesson 9: Conditions for Triangle Similarity | Practice Problems

What is the length of segment \(DF\)? Description: Triangle A B C and D E F. Measurements are as follows: A B is 8, A C is 6, angle A is 68 degrees, angle B is 44 degrees, D E is 18, angle D is 68 degrees,and angle F is 44 degrees.

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

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

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

Must these parallelograms be similar? Explain your reasoning.

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

Quadrilaterals \(Q\) and \(P\) are similar. What is the scale factor of the dilation that takes \(P\) to \(Q\)?

• \(\frac35\)

• \(\frac45\)

• \(\frac54\)

• \(\frac53\)

The circle centered at \(Q\) is a scaled copy of the circle centered at \(R\). Find the scale factor. Find the value of \(x\).