Defining Reflections

ID: birav-pizan
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Defining Reflections

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Problem 1

1) Which of these constructions would construct a line of reflection that takes the point AA to point BB?

a) Construct the perpendicular bisector of segment AB\text{Construct the perpendicular bisector of segment } AB \text{. }b) Construct a line through B perpendicular to segment AB.\text{Construct a line through } B \text{ perpendicular to segment } AB \text{.}c) Construct the line passing through A and B\text{Construct the line passing through } A \text{ and } B \text{. }d) Construct a line parallel to line AB.\text{Construct a line parallel to line } AB \text{.}
Problem 2

2) A point PP stays in the same location when it is reflected over line ll.

What can you conclude about PP?

A template for answering this question. Ask your instructor for an alternative.
Problem 3

Lines ll and mm are perpendicular with point of intersection PP.

Noah says that a 180 degree rotation, with center PP, has the same effect on points in the plane as reflecting over line mm.

3) Do you agree with Noah?

A template for answering this question. Ask your instructor for an alternative.
a) I agree with Noah\text{I agree with Noah}b) I disagree with Noah\text{I disagree with Noah}

4) Explain your reasoning.

Problem 4

5) Here are 4 triangles that have each been transformed by a different transformation. Which transformation is not a rigid transformation?

A template for answering this question. Ask your instructor for an alternative.
a) Transformation A\text{Transformation A}b) Transformation B\text{Transformation B}c) Transformation C\text{Transformation C}d) Transformation D\text{Transformation D}
Problem 5

6) There is a sequence of rigid transformations that takes AA to AA', BB to BB', and CC to CC'. The same sequence takes DD to DD'. Draw and label DD':

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Problem 6

7) Here are 3 points in the plane. Explain how to determine whether point CC is closer to point AA or point BB.

A template for answering this question. Ask your instructor for an alternative.
Problem 7

8) Diego says a quadrilateral with 4 congruent sides is always a regular polygon. Mai say it never is one. Do you agree with either of them?

a) I agree with Diego\text{I agree with Diego}b) I agree with Mai\text{I agree with Mai}c) I agree with both of them\text{I agree with both of them}d) I disagree with both of them\text{I disagree with both of them}