# Lesson 21

One Hundred and Eighty

### Problem 1

The triangles here are each obtained by applying rigid motions to triangle 1.

- Which triangles are translations of triangle 1? Explain how you know.
- Which triangles are not translations of triangle 1? Explain how you know.

### Problem 2

The quadrilateral is a parallelogram. Find the measure of angles 1, 2, and 3.

### Problem 3

In the figure shown, lines \(f\) and \(g\) are parallel. Select the angle that is congruent to angle 1.

Angle 2

Angle 6

Angle 7

Angle 8

### Problem 4

Angle \(BDE\) is congruent to angle \(BAC\). Name another pair of congruent angles. Explain how you know.

### Problem 5

- Describe a transformation that could be used to show that corresponding angles are congruent.
- Describe a transformation that could be used to show that alternate interior angles are congruent.

### Problem 6

Lines \(AD\) and \(EC\) meet at point \(B\).

Which of these *must* be true? Select **all** that apply.

A 180 degree clockwise rotation using center $B$ takes $D$ to $A$.

The image of $D$ after a 180 degree rotation using center $B$ lies on ray $BA$.

If a 180 degree rotation using center $B$ takes $C$ to $E$ then it also takes $E$ to $C$.

Angle $ABC$ is congruent to angle $DBE$.

Angle $ABE$ is congruent to angle $ABC$.

### Problem 7

Points \(E\), \(B\), and \(C\) are collinear. Explain why points \(A\), \(B\), and \(D\) are collinear.

### Problem 8

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

### Problem 9

Triangle \(ABC\) is congruent to triangle \(A’B’C’\). Describe a sequence of rigid motions that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\).