# Congruent Parts, Part 2

ID: miduk-lubik Illustrative Mathematics, CC BY 4.0
Subject: Geometry

12 questions

# Congruent Parts, Part 2

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##### Problem 1

Line ﻿$SD$﻿ is a line of symmetry for figure ﻿$AXPDZHMS$﻿. Noah says that ﻿$AXPDS$﻿ is congruent to ﻿$HMZDS$﻿ because sides ﻿$AX$﻿ and ﻿$HM$﻿ are corresponding. 1) Why is Noah’s congruence statement incorrect?

2) What pentagon is congruent to pentagon ﻿$AXPDS$﻿?

##### Problem 2

Figure ﻿$MBJKGH$﻿ is the image of figure ﻿$AFEKJB$﻿ after being rotated 90 degrees counterclockwise about point ﻿$K$﻿. 3) Draw a segment in figure ﻿$AFEKJB$﻿ to create a quadrilateral. 4) Draw the image of the segment when rotated 90 degrees counterclockwise about point ﻿$K$﻿. 5) Write a congruence statement for the quadrilateral you created in figure ﻿$AFEKJB$﻿ and the image of the quadrilateral in figure ﻿$MBJKGH$﻿.

##### Problem 3

6) Triangle ﻿$HEF$﻿ is the image of triangle ﻿$FGH$﻿ after a 180 degree rotation about point ﻿$K$﻿.

Select ﻿$\textbf{all}$﻿ 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 ﻿$KHE$﻿ is congruent to angle ﻿$KFG$﻿. ﻿$\quad\quad$﻿ d) Angle ﻿$GHK$﻿ is congruent to angle ﻿$KHE$﻿. ﻿$\quad\quad$﻿ e) Segment ﻿$EH$﻿ is congruent to segment ﻿$FG$﻿. ﻿$\quad\quad$﻿ f) Segment ﻿$GH$﻿ is congruent to segment ﻿$EF$﻿. ##### Problem 4

7) When triangle ﻿$ABC$﻿ is reflected across line ﻿$AB$﻿, the image is triangle ﻿$ABD$﻿. Why are segment ﻿$AD$﻿ and segment ﻿$AC$﻿ congruent? a)

Congruent parts of congruent figures are corresponding.

b)

Corresponding parts of congruent figures are congruent.

c)

An isosceles triangle has a pair of congruent sides.

d)

Segment ﻿$AB$﻿ is a perpendicular bisector of segment ﻿$DC$﻿.

##### Problem 5

Elena needs to prove angles ﻿$BED$﻿ and ﻿$BCA$﻿ are congruent. Provide reasons to support each of her statements. 8) Line ﻿$m$﻿ is parallel to line ﻿$l$﻿.

9) Angles ﻿$BED$﻿ and ﻿$BCA$﻿ are congruent.

##### Problem 6

10) Triangle ﻿$FGH$﻿ is the image of isosceles triangle ﻿$FEH$﻿ after a reflection across line ﻿$HF$﻿. Select ﻿$\textbf{all}$﻿ 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. ﻿$\quad\quad\quad$﻿ b) ﻿$EFGH$﻿ is a rhombus. ﻿$\quad\quad\quad$﻿ c) Diagonal ﻿$FH$﻿ bisects angles ﻿$EFG$﻿ and ﻿$EHG$﻿. ﻿$\quad\quad\quad$﻿d) Diagonal ﻿$FH$﻿ is perpendicular to side ﻿$FE$﻿. ﻿$\quad\quad$﻿ e) Angle ﻿$EHF$﻿ is congruent to angle ﻿$FGH$﻿. ﻿$\quad\quad$﻿ f) Angle ﻿$FEH$﻿ is congruent to angle ﻿$FGH$﻿. ##### Problem 7

This design began from the construction of a regular hexagon. 11) Draw 1 segment so the diagram has another hexagon that is congruent to hexagon ﻿$ABCIHG$﻿. 12) Explain why the hexagons are congruent.