Conditions for Triangle Similarity

ID: himor-nuzaf
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
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13 questions

Conditions for Triangle Similarity

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Problem 1

1) What is the length of segment DFDF?

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Problem 2

2) In triangle ABCABC, angle AA is 35º and angle BB is 20º. Select all\textbf{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


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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


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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

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

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?

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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.

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12) Find the scale factor.

13) Find the value of xx.