# Lesson 19

Evidence, Angles, and Proof

The practice problem answers are available at one of our IM Certified Partners

### Problem 1

What is the measure of angle $$ABE$$?

### Problem 2

Select all true statements about the figure.

A:

$c + b = d + c$

B:

$d + b = 180$

C:

Rotate clockwise by angle $ABC$ using center $B$. Then angle $CBD$ is the image of angle $ABE$.

D:

Rotate 180 degrees using center $B$. Then angle $CBD$ is the image of angle $EBA$.

E:

Reflect across the angle bisector of angle $ABC$. Then angle $CBD$ is the image of angle $ABE$.

F:

Reflect across line $CE$. Then angle $CBD$ is the image of angle $EBA$

### Problem 3

Point $$D$$ is rotated 180 degrees using $$B$$ as the center. Explain why the image of $$D$$ must lie on the ray $$BA$$.

### Problem 4

Draw the result of this sequence of transformations.

1. Rotate $$ABCD$$ clockwise by angle $$ADC$$ using point $$D$$ as the center.
2. Translate the image by the directed line segment $$DE$$
(From Geometry, Unit 1, Lesson 18.)

### Problem 5

Quadrilateral $$ABCD$$ is congruent to quadrilateral $$A’B’C’D’$$. Describe a sequence of rigid motions that takes $$A$$ to $$A’$$, $$B$$ to $$B’$$, $$C$$ to $$C’$$, and $$D$$ to $$D’$$.

(From Geometry, Unit 1, Lesson 17.)

### Problem 6

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 $$C’$$.

(From Geometry, Unit 1, Lesson 17.)

### Problem 7

In quadrilateral $$BADC$$, $$AB=AD$$ and $$BC=DC$$. The line $$AC$$ is a line of symmetry for this quadrilateral.

1. Based on the line of symmetry, explain why the diagonals $$AC$$ and $$BD$$ are perpendicular.
2. Based on the line of symmetry, explain why angles $$ACB$$ and $$ACD$$ have the same measure.
(From Geometry, Unit 1, Lesson 15.)

### Problem 8

Here are 2 polygons:

Select all sequences of translations, rotations, and reflections below that would take polygon $$P$$ to polygon $$Q$$.

A:

Reflect over line $BA$ and then translate by directed line segment $CB$.

B:

Translate by directed line segment $BA$ then reflect over line $BA$.

C:

Rotate $60^\circ$ clockwise around point $B$ and then translate by directed line segment $CB$.

D:

Translate so that $E$ is taken to $H$. Then rotate $120^\circ$ clockwise around point $H$.

E:

Translate so that $A$ is taken to $J$. Then reflect over line $BA$.

(From Geometry, Unit 1, Lesson 13.)