# Congruent Triangles, Part 1

ID: basur-mopor
Illustrative Mathematics
Subject: Geometry

13 questions

# Congruent Triangles, Part 1

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##### Problem 1

1) Triangle ﻿$ABC$﻿ is congruent to triangle ﻿$EDF$﻿. So, Kiran 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 ﻿$F$﻿. b) Angle ﻿$B$﻿ coincides with angle ﻿$D$﻿. c) Segment ﻿$AC$﻿ coincides with segment ﻿$EF$﻿.

d) Segment ﻿$BC$﻿ coincides with segment ﻿$ED$﻿. e) Segment ﻿$AB$﻿ coincides with segment ﻿$ED$﻿.

##### Problem 2

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

2) Explain why the image of ray ﻿$CA$﻿ lines up with ray ﻿$CE$﻿.

3) Explain why the image of ﻿$A$﻿ coincides with ﻿$E$﻿.

4) Is triangle ﻿$CBA$﻿ congruent to triangle ﻿$CDE$﻿?

True or false? Write below.

##### Problem 3

6) The triangles are congruent. Which sequence of rigid motions will take ﻿$XYZ$﻿ onto ﻿$BCA$﻿?

a) $\text{Translate } XYZ \text{ using directed line segment } YC \text{. Rotate } X'Y'Z' \text{ using } C \text{ as the center so that } X' \text{ coincides with } B \text{. } \newline \text{ Reflect } X''Y''Z'' \text{ across line } CB \text{. }$b) $\text{Translate } XYZ \text{ using directed line segment } YC \text{. Rotate } X'Y'Z' \text{ using } C \text{ as the center so that } X' \text{ coincides with } B \text{. } \newline \text{ Reflect } X''Y''Z'' \text{ across line } AC \text{. }$c) $\text{Translate } XYZ \text{ using directed line segment } YC \text{. Rotate } X'Y'Z' \text{ using } C \text{ as the center so that } X' \text{ coincides with } A \text{. } \newline \text{ Reflect } X''Y''Z'' \text{ across line } CB \text{. }$d) $\text{Translate } XYZ \text{ using directed line segment } YC \text{. Rotate } X'Y'Z' \text{ using } C \text{ as the center so that } X' \text{ coincides with } A \text{. } \newline \text{ Reflect } X''Y''Z'' \text{ across line } AC \text{. }$
##### Problem 4

7) Triangle ﻿$HEF$﻿ is the image of triangle ﻿$FGH$﻿ after a 180 degree rotation around point ﻿$K$﻿. Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Triangle ﻿$HGF$﻿ is congruent to triangle ﻿$FEH$﻿. b) Triangle ﻿$GFH$﻿ is congruent to triangle ﻿$EFH$﻿.

c) Angle ﻿$KHE$﻿ is congruent to angle ﻿$KHG$﻿. d) Angle ﻿$GHK$﻿ is congruent to angle ﻿$EFK$﻿.

e) Segment ﻿$EF$﻿ is congruent to segment ﻿$GH$﻿. f) Segment ﻿$HG$﻿ is congruent to segment ﻿$FE$﻿.

g) Segment ﻿$FH$﻿ is congruent to segment ﻿$HF$﻿.

##### Problem 5

Line ﻿$SD$﻿ is a line of symmetry for figure ﻿$ASMHZDPX$﻿. Tyler says that ﻿$ASDPX$﻿ is congruent to ﻿$SMDZH$﻿ because sides ﻿$AS$﻿ and ﻿$MS$﻿ are corresponding.

8) Why is Tyler's congruence statement incorrect?

9) Which pentagon is congruent to pentagon ﻿$ASDPX$﻿?

##### Problem 6

10) Triangle ﻿$ABC$﻿ is congruent to triangle ﻿$DEF$﻿. Select all the statements that are a result of corresponding parts of congruent triangles being congruent. Write each corresponding letter in the answer box and separate letters with commas.

a) Segment ﻿$AC$﻿ is congruent to segment ﻿$EF$﻿. b) Segment ﻿$BC$﻿ is congruent to segment ﻿$EF$﻿.

c) Angle ﻿$BAC$﻿ is congruent to angle ﻿$EDF$﻿. d) Angle ﻿$BCA$﻿ is congruent to angle ﻿$EDF$﻿.

e) Angle ﻿$CBA$﻿ is congruent to angle ﻿$DEF$﻿.

##### Problem 7

11) When triangle ﻿$ABC$﻿ is reflected across line ﻿$AB$﻿, the image is triangle ﻿$ABD$﻿. Why is angle ﻿$ACD$﻿ congruent to angle ﻿$ADB$﻿?

a) $\text{Corresponding parts of congruent figures are congruent.}$b) $\text{Congruent parts of congruent figures are corresponding.}$c) $\text{Segment } AB \text{ is a perpendicular bisector of segment } DC \text{.}$d) $\text{An isosceles triangle has a pair of congruent angles.}$
##### Problem 8

Line ﻿$DE$﻿ is parallel to line ﻿$BC$﻿.

12) What is the measure of angle ﻿$EAC$﻿?

13) What is the measure of angle ﻿$DAB$﻿?