Points, Segments, and Zigzags

ID: guhof-razod
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Points, Segments, and Zigzags

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Problem 1

1) Write a sequence of rigid motions to take figure ABCABC to figure DEFDEF.

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Problem 2

2) Prove the circle centered at AA is congruent to the circle centered at CC.

ABAB = CDCD

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Problem 3

3) Which conjecture is possible to prove?

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

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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 HEFHEF is the image of triangle HGFHGF after a reflection across line FHFH. Write a congruence statement for the 2 congruent triangles.

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Problem 6

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

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

a) Angle AA coincides with angle FF. \quad\quad\quad b) Angle BB coincides with angle DD. \quad\quad\quad c) Angle CC coincides with angle EE.

d) Segment BABA coincides with segment DEDE. \quad\quad\quad e) Segment BCBC coincides with segment FEFE.

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Problem 7

This design began from the construction of a regular hexagon.

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9) Is quadrilateral JKLOJKLO congruent to the other 2 quadrilaterals?

True or false? Write below.

10) Explain how you know.