# Rigid Transformations

ID: rakaz-panul
Illustrative Math
Subject: Geometry

# Rigid Transformations

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##### Problem 1

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

a) $\text{Figure A}$b) $\text{Figure B}$c) $\text{Figure C}$d) $\text{Figure D}$
##### Problem 2

2) What is the definition of congruence?

a) $\text{If two figures have the same shape, then they are congruent. }$b) $\text{If two figures have the same area, then they are congruent. }$c) $\text{If there is a sequence of transformations taking one figure to another, then they are congruent. }$d) $\text{If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.}$
##### Problem 3

3) 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 4

4) Three schools are located at points ﻿$A$﻿, ﻿$B$﻿, and ﻿$C$﻿. The school district wants to locate its new stadium at a location that will be roughly the same distance from all 3 schools. Where should they build the stadium?

5) Explain or show your reasoning.

##### Problem 5

6) To construct a line passing through point ﻿$C$﻿ that is parallel to the line ﻿$AB$﻿, Han constructed the perpendicular bisector of ﻿$AB$﻿ and then drew line ﻿$CD$﻿.

Is ﻿$CD$﻿ guaranteed to be parallel to ﻿$AB$﻿?

True or false? Write below.

7) Explain how you know.

##### Problem 6

8) This diagram is a straightedge and compass construction of a line perpendicular to line ﻿$AB$﻿ passing through point ﻿$C$﻿. Select all the statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$AD=BD$﻿ ﻿$\quad\quad$﻿ b) ﻿$EC=AD$﻿ ﻿$\quad\quad$﻿ c) ﻿$AC=DC$﻿ ﻿$\quad\quad$﻿ d) ﻿$EA=ED$﻿ ﻿$\quad\quad$﻿ e) ﻿$ED=DB$﻿ ﻿$\quad\quad$﻿ f) ﻿$CB=AD$﻿