# Points, Segments, and Zigzags

ID: guhof-razod
Illustrative Math
Subject: Geometry

# Points, Segments, and Zigzags

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##### 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?

a) $\text{All quadrilaterals with at least one side length of 3 are congruent.}$b) $\text{All rectangles with at least one side length of 3 are congruent.}$c) $\text{All rhombuses with at least one side length of 3 are congruent.}$d) $\text{All squares with at least one side length of 3 are congruent.}$
##### 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?

True or false? Write below.

10) Explain how you know.