# Lesson 5

Points, Segments, and Zigzags

### Problem 1

Write a sequence of rigid motions to take figure $$ABC$$ to figure $$DEF$$.

### Problem 2

Prove the circle centered at $$A$$ is congruent to the circle centered at $$C$$.

### Problem 3

Which conjecture is possible to prove?

A:

All quadrilaterals with at least one side length of 3 are congruent.

B:

All rectangles with at least one side length of 3 are congruent.

C:

All rhombuses with at least one side length of 3 are congruent.

D:

All squares with at least one side length of 3 are congruent.

### Problem 4

Match each statement using only the information shown in the pairs of congruent triangles.

### Solution

(From Unit 2, Lesson 4.)

### Problem 5

Triangle $$HEF$$ is the image of triangle $$HGF$$ after a reflection across line $$FH$$. Write a congruence statement for the 2 congruent triangles.

### Solution

(From Unit 2, Lesson 2.)

### Problem 6

Triangle $$ABC$$ is congruent to triangle $$EDF$$. So, Lin knows that there is a sequence of rigid motions that takes $$ABC$$ to $$EDF$$.

Select all true statements after the transformations:

A:

Angle $$A$$ coincides with angle $$F$$.

B:

Angle $$B$$ coincides with angle $$D$$.

C:

Angle $$C$$ coincides with angle $$E$$.

D:

Segment $$BA$$ coincides with segment $$DE$$.

E:

Segment $$BC$$ coincides with segment $$FE$$.

### Solution

This design began from the construction of a regular hexagon. Is quadrilateral $$JKLO$$ congruent to the other 2 quadrilaterals? Explain how you know.