Evidence, Angles, and Proof

ID: zobar-votud
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Evidence, Angles, and Proof

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Problem 1

1) What is the measure of angle ABEABE?

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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+cc + d = d + c \quad\quad\quad b) d+b=180d + b = 180

c) Rotate clockwise by angle ABCABC using center BB. Then angle CBDCBD is the image of angle ABEABE.

d) Rotate 180 degrees using center BB. Then angle CBDCBD is the image of angle EBAEBA.

e) Reflect across the angle bisector of angle ABCABC. Then angle CBDCBD is the image of angle ABEABE.

f) Reflect across line CECE. Then angle CBDCBD is the image of angle EBAEBA.

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Problem 3

3) Point DD is rotated 180 degrees using BB as the center. Explain why the image of DD must lie on the ray BABA.

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Problem 4

4) Draw the result of this sequence of transformations.

1) Rotate ABCDABCD clockwise by angle ADCADC using point DD as the center.

2) Translate the image by the directed line segment DEDE.

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Problem 5

5) Quadrilateral ABCDABCD is congruent to quadrilateral ABCDA'B'C'D'. Describe a sequence of rigid motions that takes AA to AA', BB to BB', CC to CC', and DD to DD'.

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Problem 6

6) Triangle ABCABC is congruent to triangle ABCA'B'C'. Describe a sequence of rigid motions that takes AA to AA', BB to BB', and CC to CC'.

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Problem 7

In quadrilateral BADCBADC, AB=ADAB = AD and BC=DCBC = DC. The line ACAC is a line of symmetry for this quadrilateral.

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7) Based on the line of symmetry, explain why the diagonals ACAC and BDBD are perpendicular.

8) Based on the line of symmetry, explain why angles ACBACB and ACDACD have the same measure.

Problem 8

9) Below are 2 polygons.

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

a) Reflect over line BABA and then translate by directed line segment CBCB.

b) Translate by directed line segment BABA then reflect over line BABA.

c) Rotate 6060^{\circ} clockwise around point BB and then translate by directed line segment CBCB.

d) Translate so that EE is taken to HH. Then rotate 120120^{\circ} clockwise around point HH.

e) Translate so that AA is taken to JJ. Then reflect over line BABA.

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