# Evidence, Angles, and Proof

ID: zobar-votud Illustrative Math
Subject: Geometry

# Evidence, Angles, and Proof

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##### 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 ﻿$BA$﻿. 