# Lesson 15

Symmetry

- Let’s describe some symmetries of shapes.

### 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.

- Based on the line of symmetry, explain why the diagonals \(AC\) and \(BD\) are perpendicular.
- 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.

### 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 \(B\)?

\(45^\circ\)

\(60^\circ\)

\(90^\circ\)

\(180^\circ\)

### 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 \(D\).

### 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

B

C

D

E

### Problem 7

Here is triangle \(POG\). Match the description of the rotation with the image of \(POG\) under that rotation.