Conditions for Triangle Similarity

ID: fusoj-varon
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Conditions for Triangle Similarity

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

1) What is the length of segment DFDF?

A template for answering this question. Ask your instructor for an alternative.
Problem 2

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

a) Triangle DEFDEF where angle DD is 35°35\degree and angle EE is 20°20\degree.\quadb) Triangle GHIGHI where angle GG is 35°35\degree and angle II is 30°30\degree.

c) Triangle JKLJKL where angle JJ is 35°35\degree and angle LL is 125°125\degree.\quadd) Triangle MNOMNO where angle NN is 20°20\degree and angle OO is 125°125\degree.

e) Triangle PQRPQR where angle QQ is 20°20\degree and angle RR is 30°30\degree.

Problem 3


A template for answering this question. Ask your instructor for an alternative.

3) Are triangles ABCABC and DECDEC 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


A template for answering this question. Ask your instructor for an alternative.

6) Must these parallelograms be similar?

True or false? Write below.

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.

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

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

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

10) Explain or show your reasoning.

Problem 7

11) Quadrilaterals QQ and PP are similar. What is the scale factor of the dilation that takes PP to QQ?

A template for answering this question. Ask your instructor for an alternative.
a) 35 \frac{3}{5} b) 45 \frac{4}{5} c) 54 \frac{5}{4} d) 53 \frac{5}{3}
Problem 8

The circle centered at QQ is a scaled copy of the circle centered at RR.

A template for answering this question. Ask your instructor for an alternative.

12) Find the scale factor.

13) Find the value of xx.