# Congruent Triangles, Part 2

ID: hiboz-tiron
Illustrative Math
Subject: Geometry

# Congruent Triangles, Part 2

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##### Problem 1

Match each statement using only the information shown in the images of pairs of congruent triangles. Write the number of the corresponding image in the answer box.

1) In the 2 triangles there are 3 pairs of congruent sides.

2) The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

3) The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

##### Problem 2

4) Sketch the unique triangles that can be made with angle measures ﻿$40\degree$﻿ and ﻿$100\degree$﻿ and side length 3.

5) How do you know you have sketched all possibilities?

##### Problem 3

6) What is the least amount of information that you need to construct a triangle congruent to this one?

##### Problem 4

7) Triangle ﻿$ABC$﻿ is congruent to triangle ﻿$EDF$﻿. So, Mai knows that there is a sequence of rigid motions that takes ﻿$ABC$﻿ to ﻿$EDF$﻿.

Select all true statements after the transformations. Write each corresponding letter in the answer box and separate letters with commas.

a) Angle ﻿$A$﻿ coincides with angle ﻿$E$﻿. ﻿$\quad\quad$﻿ b) Angle ﻿$B$﻿ coincides with angle ﻿$F$﻿. ﻿$\quad\quad$﻿ c) Segment ﻿$AB$﻿ coincides with segment ﻿$EF$﻿. ﻿$\quad\quad$﻿ d) Segment ﻿$BC$﻿ coincides with segment ﻿$DF$﻿. ﻿$\quad\quad$﻿ e) Segment ﻿$AC$﻿ coincides with segment ﻿$ED$﻿.

##### Problem 5

A rotation by angle ﻿$ACE$﻿ using point ﻿$C$﻿ as the center takes triangle ﻿$CBA$﻿ onto triangle ﻿$CDE$﻿.

8) Explain why the image of segment ﻿$CB$﻿ lines up with ray ﻿$CD$﻿.

9) Explain why the image of ﻿$B$﻿ coincides with ﻿$D$﻿.

10) Is triangle ﻿$ABC$﻿ congruent to triangle ﻿$EDC$﻿?

True or false? Write below.

##### Problem 6

Line ﻿$EF$﻿ is a line of symmetry for figure ﻿$ABECDF$﻿. Clare says that ﻿$ABEF$﻿ is congruent to ﻿$CDFE$﻿ because sides ﻿$AB$﻿ and ﻿$CD$﻿ are corresponding.

12) Why is Clare's congruence statement incorrect?

13) Write a correct congruence statement for the quadrilaterals.

##### Problem 7

14) Triangle ﻿$HEF$﻿ is the image of triangle ﻿$HGF$﻿ after a reflection across line ﻿$FH$﻿.

Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Triangle ﻿$FGH$﻿ is congruent to triangle ﻿$FEH$﻿. ﻿$\quad\quad$﻿ b) Triangle ﻿$EFH$﻿ is congruent to triangle ﻿$GFH$﻿. ﻿$\quad\quad$﻿ c) Angle ﻿$HFE$﻿ is congruent to angle ﻿$FHG$﻿. ﻿$\quad\quad$﻿ d) Angle ﻿$EFG$﻿ is congruent to angle ﻿$EHG$﻿. ﻿$\quad\quad$﻿ e) Segment ﻿$EH$﻿ is congruent to segment ﻿$FG$﻿. ﻿$\quad\quad$﻿ f) Segment ﻿$GH$﻿ is congruent to segment ﻿$HE$﻿.

##### Problem 8

15) When rectangle ﻿$ABCD$﻿ is reflected across line ﻿$EF$﻿, the image is ﻿$BADC$﻿. How do you know that segment ﻿$AD$﻿ is congruent to segment ﻿$BC$﻿?

a) $\text{A rectangle has 2 pairs of parallel sides.}$b) $\text{Any 2 sides of a rectangle are congruent.}$c) $\text{Corresponding parts of congruent figures are congruent.}$d) $\text{Congruent parts of congruent figures are corresponding.}$
##### Problem 9

16) This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.