Lesson 15

Symmetry

Problem 1

For each figure, identify any lines of symmetry the figure has.

Problem 2

In quadrilateral $$BADC$$, $$AB=AD$$ and $$BC=DC$$. The line $$AC$$ is a line of symmetry for this quadrilateral.

1. Based on the line of symmetry, explain why the diagonals $$AC$$ and $$BD$$ are perpendicular.
2. Based on the line of symmetry, explain why angles $$ABC$$ and $$ADC$$ have the same measure.

Problem 3

Three line segments form the letter Z. Rotate the letter Z counterclockwise around the midpoint of segment $$BC$$ by 180 degrees. Describe the result.

Solution

(From Unit 1, Lesson 14.)

Problem 4

There is a square, $$ABCS$$, inscribed in a circle with center $$D$$. What is the smallest angle we can rotate around $$D$$ so that the image of $$A$$ is $$B$$?

A:

$$45^\circ$$

B:

$$60^\circ$$

C:

$$90^\circ$$

D:

$$180^\circ$$

Solution

(From Unit 1, Lesson 14.)

Problem 5

Points $$A$$, $$B$$, $$C$$, and $$D$$ are vertices of a square.  Point $$E$$ is inside the square. Explain how to tell whether point $$E$$ is closer to $$A$$, $$B$$, $$C$$, or $$D$$.

Solution

(From Unit 1, Lesson 9.)

Problem 6

Lines $$\ell$$ and $$m$$ are perpendicular.

Sometimes reflecting a point over $$m$$ has the same effect as rotating the point 180 degrees using center $$P$$. Select all labeled points which have the same image for both transformations.

A:

A

B:

B

C:

C

D:

D

E:

E

Solution

Here is triangle $$POG$$. Match the description of the rotation with the image of $$POG$$ under that rotation.