# Now What Can You Build?

# Now What Can You Build?

##### 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?

4) Explain your reasoning.

##### 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.