Conditions for Triangle Similarity

ID: himor-nuzaf
Illustrative Mathematics, CC BY 4.0
Subject: Geometry

13 questions

Conditions for Triangle Similarity

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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?

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

6) Must these parallelograms be similar?

True or false? Write below.

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 ﻿$Q$﻿ and ﻿$P$﻿ are similar. What is the scale factor of the dilation that takes ﻿$P$﻿ to ﻿$Q$﻿?

a)

﻿$\frac{3}{5}$﻿

b)

﻿$\frac{4}{5}$﻿

c)

﻿$\frac{5}{4}$﻿

d)

﻿$\frac{5}{3}$﻿

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 ﻿$x$﻿.