# Lesson 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. Write a correct congruence statement for the pentagons.

### Problem 2

FIgure $$MBJKGH$$ is the image of figure $$AFEKJB$$ after being rotated 90 degrees counterclockwise about point $$K$$. Draw a segment in figure $$AFEKJB$$ to create a quadrilateral. Draw the image of the segment when rotated 90 degrees counterclockwise about point $$K$$

Write a congruence statement for the quadrilateral you created in figure $$AFEKJB$$ and the image of the quadrilateral in figure $$MBJKGH$$.

### Problem 3

Triangle $$HEF$$ is the image of triangle $$FGH$$ after a 180 degree rotation about point $$K$$. Select all statements that must be true.

A:

Triangle $$FGH$$ is congruent to triangle $$FEH$$.

B:

Triangle $$EFH$$ is congruent to triangle $$GFH$$.

C:

Angle $$KHE$$ is congruent to angle $$KFG$$.

D:

Angle $$GHK$$ is congruent to angle $$KHE$$.

E:

Segment $$EH$$ is congruent to segment $$FG$$.

F:

Segment $$GH$$ is congruent to segment $$EF$$.

### Problem 4

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 $$DC$$.

### Solution

(From Unit 2, Lesson 1.)

### Problem 5

Elena needs to prove angles $$BED$$ and $$BCA$$ are congruent. Provide reasons to support each of her statements.

1. Line $$m$$ is parallel to line $$l$$.
2. Angles $$BED$$ and $$BCA$$ are congruent.

### Solution

(From Unit 1, Lesson 20.)

### Problem 6

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.

A:

$$EFGH$$ is a rectangle.

B:

$$EFGH$$ is a rhombus.

C:

Diagonal $$FH$$ bisects angles $$EFG$$ and $$EHG$$.

D:

Diagonal $$FH$$ is perpendicular to side $$FE$$.

E:

Angle $$EHF$$ is congruent to angle $$FGH$$.

F:

Angle $$FEH$$ is congruent to angle $$FGH$$.

### Solution

(From Unit 2, Lesson 1.)

### Problem 7

This design began from the construction of a regular hexagon.

1. Draw 1 segment so the diagram has another hexagon that is congruent to hexagon $$ABCIHG$$.
2. Explain why the hexagons are congruent.