# Points, Segments, and Zigzags

# Points, Segments, and Zigzags

##### Problem 1

1) Write a sequence of rigid motions to take figure $ABC$ to figure $DEF$.

##### Problem 2

2) Prove the circle centered at $A$ is congruent to the circle centered at $C$.

$AB$ = $CD$

##### Problem 3

3) Which conjecture is possible to prove?

##### Problem 4

Match each statement using only the information shown in the pairs of congruent triangles. Write the number of the corresponding pair of congruent triangles in the answer box.

4) The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

5) The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

6) In the 2 triangles there are 3 pairs of congruent sides.

##### Problem 5

7) Triangle $HEF$ is the image of triangle $HGF$ after a reflection across line $FH$. Write a congruence statement for the 2 congruent triangles.

##### Problem 6

8) Triangle $ABC$ is congruent to triangle $EDF$. So, Lin knows that there is a sequence of rigid motions that takes $ABC$ to $EDF$.

Select **all** true statements after the transformations. Write each corresponding letter in the answer box and separate letters with commas.

a) Angle $A$ coincides with angle $F$. $\quad\quad\quad$ b) Angle $B$ coincides with angle $D$. $\quad\quad\quad$ c) Angle $C$ coincides with angle $E$.

d) Segment $BA$ coincides with segment $DE$. $\quad\quad\quad$ e) Segment $BC$ coincides with segment $FE$.

##### Problem 7

This design began from the construction of a regular hexagon.

9) Is quadrilateral $JKLO$ congruent to the other 2 quadrilaterals?

10) Explain how you know.