Congruent Parts, Part 1

ID: kimum-fuboz
Illustrative Math
Subject: Geometry

Congruent Parts, Part 1

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Problem 1

1) When rectangle ﻿$ABCD$﻿ is reflected across line ﻿$EF$﻿, the image is ﻿$DCBA$﻿. How do you know that segment ﻿$AB$﻿ is congruent to segment ﻿$DC$﻿?

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

2) Triangle ﻿$FGH$﻿ is the image of isosceles triangle ﻿$FEH$﻿ after a reflection across line ﻿$HF$﻿. 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) ﻿$EFGH$﻿ is a rectangle. ﻿$\quad\quad$﻿ b) ﻿$EFGH$﻿ has 4 congruent sides. ﻿$\quad\quad$﻿ c) Diagonal ﻿$FH$﻿ bisects angles ﻿$EFG$﻿ and ﻿$EHG$﻿.

d) Diagonal ﻿$FH$﻿ is perpendicular to side ﻿$FE$﻿. ﻿$\quad\quad$﻿ e) Angle ﻿$FEH$﻿ is congruent to angle ﻿$FGH$﻿.

Problem 3

3) Reflect right triangle ﻿$ABC$﻿ across line ﻿$BC$﻿.

4) Classify triangle ﻿$ACA'$﻿ according to its side lengths.

5) Explain how you know.

Problem 4

6) Triangles ﻿$FAD$﻿ and ﻿$DCE$﻿ are translations of triangle ﻿$ABC$﻿.

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

a) Points ﻿$B$﻿, ﻿$A$﻿, and ﻿$F$﻿ are collinear. ﻿$\quad\quad$﻿ b) The measure of angle ﻿$BCA$﻿ is the same as the measure of angle ﻿$CED$﻿.

c) Line ﻿$AD$﻿ is parallel to line ﻿$BC$﻿. ﻿$\quad\quad$﻿ d) The measure of angle ﻿$CED$﻿ is the same as the measure of angle ﻿$FAD$﻿.

e) The measure of angle ﻿$DAC$﻿ is the same as the measure of angle ﻿$BCA$﻿.

f) Triangle ﻿$ADC$﻿ is a reflection of triangle ﻿$FAD$﻿.

Problem 5

Triangle ﻿$ABC$﻿ is congruent to triangles ﻿$BAD$﻿ and ﻿$CEA$﻿.

7) Explain why points ﻿$D$﻿, ﻿$A$﻿, and ﻿$E$﻿ are collinear.

8) Explain why line ﻿$DE$﻿ is parallel to line ﻿$BC$﻿.

Problem 6

9) Identify a figure that is the result of a rigid transformation of quadrilateral ﻿$ABCD$﻿.

10) Describe a rigid transformation that would take ﻿$ABCD$﻿ to that figure.