# 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.

### 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.

### Problem 5

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

Lines \(f\) and \(g\) are parallel.

Angle 2 is congruent to angle 6

Angle 2 and angle 5 are supplementary

Angle 1 is congruent to angle 7

Angle 4 is congruent to angle 6

### 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 \(M\).

- Explain why rotating \(180^\circ\) using center \(M\) takes \(A\) to \(C\).
- Explain why angles \(BAC\) and \(B’CA\) have the same measure.

### Problem 7

Lines \(AB\) and \(BC\) are perpendicular. The dashed rays bisect angles \(ABD\) and \(CBD\).

Select* ***all** statements that *must *be true:

Angle \(CBF\) is congruent to angle \(DBF\)

Angle \(CBE\) is obtuse

Angle \(ABC\) is congruent to angle \(EBF\)

Angle \(DBC\) is congruent to angle \(EBF\)

Angle \(EBF\) is 45 degrees

### 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.

### Problem 9

Draw the image of triangle \(ABC\) after this sequence of rigid transformations.

- Reflect across line segment \(AB\).
- Translate by directed line segment \(u\).

### Problem 10

- Draw the image of figure \(CAST\) after a clockwise rotation around point \(T\) using angle \(CAS\) and then a translation by directed line segment \(AS\).
- Describe another sequence of transformations that will result in the same image.