# Now What Can You Build?

ID: mukid-vifup Illustrative Math
Subject: Geometry

# Now What Can You Build?

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##### Problem 1

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

2) This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure to itself. ##### Problem 3

Noah starts with triangle ﻿$ABC$﻿ and makes 2 new triangles by translating ﻿$B$﻿ to ﻿$A$﻿ and by translating ﻿$B$﻿ to ﻿$C$﻿. Noah thinks that triangle ﻿$DCA$﻿ is congruent to triangle ﻿$BAC$﻿. 3) Do you agree with Noah?

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

##### Problem 4

In the image, triangle ﻿$ABC$﻿ is congruent to triangle ﻿$BAD$﻿ and triangle ﻿$CEA$﻿. What are the measures of the 3 angles in triangle ﻿$CEA$﻿? 5) Angle ﻿$ACE$﻿:

6) Angle ﻿$EAC$﻿:

7) Angle ﻿$CEA$﻿:

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 ﻿$f$﻿ and ﻿$g$﻿ 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. ##### Problem 6

In this diagram, point ﻿$M$﻿ is the midpoint of segment ﻿$AC$﻿ and ﻿$B'$﻿ is the image of ﻿$B$﻿ by a rotation of ﻿$180^{\circ}$﻿ around ﻿$M$﻿. 10) Explain why rotating ﻿$180^{\circ}$﻿ using center ﻿$M$﻿ takes ﻿$A$﻿ to ﻿$C$﻿.

11) Explain why angles ﻿$BAC$﻿ and ﻿$B'CA$﻿ have the same measure.

##### Problem 7

12) Lines ﻿$AB$﻿ and ﻿$BC$﻿ are perpendicular. The dashed rays bisect angles ﻿$ABD$﻿ and ﻿$CBD$﻿.

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

a) Angle ﻿$CBF$﻿ is congruent to angle ﻿$DBF$﻿ ﻿$\quad\quad$﻿ b) Angle ﻿$CBE$﻿ is obtuse ﻿$\quad\quad$﻿ c) Angle ﻿$ABC$﻿ is congruent to angle ﻿$EBF$﻿

d) Angle ﻿$DBC$﻿ is congruent to angle ﻿$EBF$﻿ ﻿$\quad\quad$﻿ e) Angle ﻿$EBF$﻿ is 45 degrees ##### Problem 8

13) Lines ﻿$AD$﻿ and ﻿$EC$﻿ meet at point ﻿$B$﻿.

Give an example of a rotation using an angle greater than 0 degrees and less than 360 degrees, that takes both lines to themselves. 14) Explain why your rotation works.

##### Problem 9

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

1) Reflect across line segment ﻿$AB$﻿.

2) Translate by directed line segment ﻿$u$﻿. ##### Problem 10

16) Draw the image of figure ﻿$CAST$﻿ after a clockwise rotation around point ﻿$T$﻿ using angle ﻿$CAS$﻿ and then a translation by directed line segment ﻿$AS$﻿. 17) Describe another sequence of transformations that will result in the same image.