# Rigid Transformations

# Rigid Transformations

##### 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?

##### Problem 2

2) What is the definition of congruence?

##### 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 $AB$?

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) $CB=AD$