# Defining Reflections

ID: birav-pizan Illustrative Math
Subject: Geometry

# Defining Reflections

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##### Problem 1

1) Which of these constructions would construct a line of reflection that takes the point ﻿$A$﻿ to point ﻿$B$﻿?

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

2) A point ﻿$P$﻿ stays in the same location when it is reflected over line ﻿$l$﻿.

What can you conclude about ﻿$P$﻿? ##### Problem 3

Lines ﻿$l$﻿ and ﻿$m$﻿ are perpendicular with point of intersection ﻿$P$﻿.

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

3) Do you agree with Noah? a) $\text{I agree with Noah}$b) $\text{I disagree with Noah}$

##### Problem 4

5) Here are 4 triangles that have each been transformed by a different transformation. Which transformation is not a rigid transformation? a) $\text{Transformation A}$b) $\text{Transformation B}$c) $\text{Transformation C}$d) $\text{Transformation D}$
##### Problem 5

6) There is a sequence of rigid transformations that takes ﻿$A$﻿ to ﻿$A'$﻿, ﻿$B$﻿ to ﻿$B'$﻿, and ﻿$C$﻿ to ﻿$C'$﻿. The same sequence takes ﻿$D$﻿ to ﻿$D'$﻿. Draw and label ﻿$D'$﻿: ##### Problem 6

7) Here are 3 points in the plane. Explain how to determine whether point ﻿$C$﻿ is closer to point ﻿$A$﻿ or point ﻿$B$﻿. ##### 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) $\text{I agree with Diego}$b) $\text{I agree with Mai}$c) $\text{I agree with both of them}$d) $\text{I disagree with both of them}$