Now What Can You Build?
1) This design began from the construction of a regular hexagon. Name 2 pairs of congruent figures.
2) This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure to itself.
Noah starts with triangle and makes 2 new triangles by translating to and by translating to . Noah thinks that triangle is congruent to triangle .
3) Do you agree with Noah?
4) Explain your reasoning.
In the image, triangle is congruent to triangle and triangle . What are the measures of the 3 angles in triangle ?
5) Angle :
6) Angle :
7) Angle :
8) Show or explain your reasoning.
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 and are parallel. b) Angle 2 is congruent to angle 6. c) Angle 2 and angle 5 are supplementary.
d) Angle 1 is congruent to angle 7. e) Angle 4 is congruent to angle 6.
In this diagram, point is the midpoint of segment and is the image of by a rotation of around .
10) Explain why rotating using center takes to .
11) Explain why angles and have the same measure.
12) Lines and are perpendicular. The dashed rays bisect angles and .
Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.
a) Angle is congruent to angle b) Angle is obtuse c) Angle is congruent to angle
d) Angle is congruent to angle e) Angle is 45 degrees
13) Lines and meet at point .
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.
15) Draw the image of triangle after this sequence of rigid transformations.
1) Reflect across line segment .
2) Translate by directed line segment .
16) Draw the image of figure after a clockwise rotation around point using angle and then a translation by directed line segment .
17) Describe another sequence of transformations that will result in the same image.