# Lesson 22

Now What Can You Build?

• Let’s construct some creative shapes.

### Problem 1

This design began from the construction of a regular hexagon. Name 2 pairs of congruent figures.

### Problem 2

This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure to itself.

### Problem 3

Noah starts with triangle $$ABC$$ and makes 2 new triangles by translating $$B$$ to $$A$$ and by translating $$B$$ to $$C$$. Noah thinks that triangle $$DCA$$  is congruent to triangle $$BAC$$. Do you agree with Noah? Explain your reasoning.

(From Unit 1, Lesson 21.)

### Problem 4

In the image, triangle $$ABC$$ is congruent to triangle $$BAD$$ and triangle $$CEA$$. What are the measures of the 3 angles in triangle $$CEA$$? Show or explain your reasoning.

(From Unit 1, Lesson 21.)

### Problem 5

In the figure shown, angle 3 is congrent to angle 6. Select all statements that must be true.

A:

Lines $$f$$ and $$g$$ are parallel.

B:

Angle 2 is congruent to angle 6

C:

Angle 2 and angle 5 are supplementary

D:

Angle 1 is congruent to angle 7

E:

Angle 4 is congruent to angle 6

(From Unit 1, Lesson 20.)

### Problem 6

In this diagram, point $$M$$ is the midpoint of segment $$AC$$ and $$B’$$ is the image of $$B$$ by a rotation of $$180^\circ$$ around $$M$$.

1. Explain why rotating $$180^\circ$$ using center $$M$$ takes $$A$$ to $$C$$.
2. Explain why angles $$BAC$$ and $$B’CA$$ have the same measure.
(From Unit 1, Lesson 20.)

### Problem 7

Lines $$AB$$ and $$BC$$ are perpendicular. The dashed rays bisect angles $$ABD$$ and $$CBD$$.

Select all statements that must be true:

A:

Angle $$CBF$$ is congruent to angle $$DBF$$

B:

Angle $$CBE$$ is obtuse

C:

Angle $$ABC$$ is congruent to angle $$EBF$$

D:

Angle $$DBC$$ is congruent to angle $$EBF$$

E:

Angle $$EBF$$ is 45 degrees

(From Unit 1, Lesson 19.)

### Problem 8

Lines $$AD$$ and $$EC$$ meet at point $$B$$.

Give an example of a rotation using an angle greater than 0 degrees and less than 360 degrees, that takes both lines to themselves. Explain why your rotation works.

(From Unit 1, Lesson 19.)

### Problem 9

Draw the image of triangle $$ABC$$ after this sequence of rigid transformations.

1. Reflect across line segment $$AB$$.
2. Translate by directed line segment $$u$$.
(From Unit 1, Lesson 18.)

### Problem 10

1. Draw the image of figure $$CAST$$ after a clockwise rotation around point $$T$$ using angle $$CAS$$ and then a translation by directed line segment $$AS$$.
2. Describe another sequence of transformations that will result in the same image.
(From Unit 1, Lesson 18.)