# Conditions for Triangle Similarity

ID: tijuz-danoj
Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Standards: HSG-SRT.A.3HSG-CO.B.8HSG-SRT.A.2HSG-CO.C.10

12 questions

# Conditions for Triangle Similarity

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##### Math Talk: Angle-Side-Angle As A Helpful Tool

How could you justify each statement?

1) Triangle ﻿$P'Q'R'$﻿ is congruent to triangle ﻿$STU$﻿.

2) Triangle ﻿$PQR$﻿ is similar to triangle ﻿$STU$﻿.

3) Triangle ﻿$G'H'I'$﻿ is congruent to triangle ﻿$MNO$﻿.

4) Triangle ﻿$GHI$﻿ is similar to triangle ﻿$MNO$﻿.

##### How Many Pieces?

For each problem, draw 2 triangles that have the listed properties. Try to make them as different as possible.

5) One angle is 45 degrees.

6) One angle is 45 degrees and another angle is 30 degrees.

7) One angle is 45 degrees and another angle is 30 degrees. The lengths of a pair of corresponding sides are 2 cm and 6 cm.

8) Select ﻿$\textbf{all}$﻿ pairs of triangles that appear to be similar? Write each corresponding letter in the answer box and separate letters with commas.

a) The pair that have only one angle in common, 45 degrees.

b) The pair that have two angles in common, 45 degrees and 30 degrees.

c) The pair that have two angles in common, 45 degrees and 30 degrees, and corresponding sides of lengths 2 cm and 6 cm.

9) Make and prove a conjecture based on your conclusions about information that leads to similar triangles.

##### Any Two Angles?

Here are 2 triangles. One triangle has a 60 degree angle and a 40 degree angle. The other triangle has a 40 degree angle and an 80 degree angle.

10) Explain how you know the triangles are similar.

11) How long is the side labeled ﻿$x$﻿?

12) How long is the side labeled ﻿$y$﻿?