# Congruent Parts, Part 2

# Congruent Parts, Part 2

##### 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 **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?

##### 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 **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.