Unit 1, Lesson 19

Evidence, Angles, and Proof

Geometry

Practice

Problem 1

What is the measure of angle ?

<p>Line segment AD is intersected at Point B by line segment EC. Measurement of Angle CBD is 40 degrees.</p>

Practice

Problem 2

Select all true statements about the figure.

<p>Line segment AD intersects line segment EC at point B. Angle EBD is labeled Angle a, Angle DBC is labeled Angle b, Angle ABC is labeled Angle C, and Angle ABE is labeled Angle d.</p>

Rotate clockwise by angle using center . Then angle is the image of angle .
Rotate 180 degrees using center . Then angle is the image of angle .
Reflect across the angle bisector of angle . Then angle is the image of angle .
Reflect across line . Then angle is the image of angle .

Problem 3

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

<p>Line segment AD is intersected at Point B by line segment EC.</p>

Problem 4

ForLesson 18: Practicing Point-by-Point Transformations

Draw the result of this sequence of transformations.

Rotate clockwise by angle using point as the center.
Translate the image by the directed line segment .

Problem 5

ForLesson 17: Working with Rigid Transformations

Quadrilateral is congruent to quadrilateral . Describe a sequence of rigid motions that takes to , to , to , and to .

<p>Two congruent quadrilaterals labeled A’B’C’D’ and ABCD. </p>

Problem 6

ForLesson 17: Working with Rigid Transformations

Triangle is congruent to triangle . Describe a sequence of rigid motions that takes to , to , and to .

<p>Two congruent triangles labeled ABC and A prime B prime C prime.</p>

Problem 7

ForLesson 15: Symmetry

In quadrilateral , and . The line is a line of symmetry for this quadrilateral.

<p>Quadrilateral B A D C, upside down kite. Starting at the bottom vertex and moving clockwise, A, D, C, B.</p>

Based on the line of symmetry, explain why the diagonals and are perpendicular.
Based on the line of symmetry, explain why angles and have the same measure.

Problem 8

ForLesson 13: Incorporating Rotations

Here are 2 polygons:

<p>5-sided polygons, P and Q, on an isometric grid. Q is a transformation of P. P has vertices A, B, C, D, and E. Q has vertices J, A, F, G, and H.</p>

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

Reflect over line . Then translate by directed line segment .

Translate by directed line segment . Then reflect over line .

Rotate clockwise around point . Then translate by directed line segment .

Translate so that is taken to . Then rotate clockwise around point .

Translate so that is taken to . Then reflect over line .

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Evidence, Angles, and Proof

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8