# Evidence, Angles, and Proof

# Evidence, Angles, and Proof

##### Problem 1

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

##### Problem 2

2) Select **all** true statements about the figure. Write each corresponding letter in the answer box and separate letters with commas.

a) $c + d = d + c$ $\quad\quad\quad$ 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

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

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 $DE$.

##### Problem 5

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 $D'$.

##### Problem 6

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 $C'$.

##### Problem 7

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

7) Based on the line of symmetry, explain why the diagonals $AC$ and $BD$ are perpendicular.

8) Based on the line of symmetry, explain why angles $ACB$ and $ACD$ have the same measure.

##### Problem 8

9) Below are 2 polygons.

Select **all** sequences of translations, rotations, and reflections below that would take polygon $P$ to polygon $Q$. Write each corresponding letter in the answer box and separate letters with commas.

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 $BA$.