Now What Can You Build?

ID: mukid-vifup
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Now What Can You Build?

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

1) This design began from the construction of a regular hexagon. Name 2 pairs of congruent figures.

A template for answering this question. Ask your instructor for an alternative.
Problem 2

2) This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure to itself.

A template for answering this question. Ask your instructor for an alternative.
Problem 3

Noah starts with triangle ABCABC and makes 2 new triangles by translating BB to AA and by translating BB to CC. Noah thinks that triangle DCADCA is congruent to triangle BACBAC.

A template for answering this question. Ask your instructor for an alternative.

3) Do you agree with Noah?

a) I agree with Noah\text{I agree with Noah}b) I disagree with Noah\text{I disagree with Noah}

4) Explain your reasoning.

Problem 4

In the image, triangle ABCABC is congruent to triangle BADBAD and triangle CEACEA. What are the measures of the 3 angles in triangle CEACEA?

A template for answering this question. Ask your instructor for an alternative.

5) Angle ACEACE:

6) Angle EACEAC:

7) Angle CEACEA:

8) Show or explain your reasoning.

Problem 5

9) In the figure shown, angle 3 is congruent to angle 6. Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Lines ff and gg are parallel. \quad\quad b) Angle 2 is congruent to angle 6. \quad\quad c) Angle 2 and angle 5 are supplementary.

d) Angle 1 is congruent to angle 7. \quad\quad e) Angle 4 is congruent to angle 6.

A template for answering this question. Ask your instructor for an alternative.
Problem 6

In this diagram, point MM is the midpoint of segment ACAC and BB' is the image of BB by a rotation of 180180^{\circ} around MM.

A template for answering this question. Ask your instructor for an alternative.

10) Explain why rotating 180180^{\circ} using center MM takes AA to CC.

11) Explain why angles BACBAC and BCAB'CA have the same measure.

Problem 7

12) Lines ABAB and BCBC are perpendicular. The dashed rays bisect angles ABDABD and CBDCBD.

Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Angle CBFCBF is congruent to angle DBFDBF \quad\quad b) Angle CBECBE is obtuse \quad\quad c) Angle ABCABC is congruent to angle EBFEBF

d) Angle DBCDBC is congruent to angle EBFEBF \quad\quad e) Angle EBFEBF is 45 degrees

A template for answering this question. Ask your instructor for an alternative.
Problem 8

13) Lines ADAD and ECEC meet at point BB.


Give an example of a rotation using an angle greater than 0 degrees and less than 360 degrees, that takes both lines to themselves.

A template for answering this question. Ask your instructor for an alternative.

14) Explain why your rotation works.

Problem 9

15) Draw the image of triangle ABCABC after this sequence of rigid transformations.

1) Reflect across line segment ABAB.

2) Translate by directed line segment uu.

A template for answering this question. Ask your instructor for an alternative.
Problem 10

16) Draw the image of figure CASTCAST after a clockwise rotation around point TT using angle CASCAS and then a translation by directed line segment ASAS.

A template for answering this question. Ask your instructor for an alternative.

17) Describe another sequence of transformations that will result in the same image.