# Symmetry

ID: domun-nabij Illustrative Math
Subject: Geometry

# Symmetry

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##### Problem 1

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

1) 2) 3) ##### Problem 2

In quadrilateral ﻿$BADC$﻿, ﻿$AB = AD$﻿ and ﻿$BC = DC$﻿. The line ﻿$AC$﻿ is a line of symmetry for this quadrilateral. 4) Based on the line of symmetry, explain why the diagonals ﻿$AC$﻿ and ﻿$BD$﻿ are perpendicular.

5) Based on the line of symmetry, explain why angles ﻿$ABC$﻿ and ﻿$ADC$﻿ have the same measure.

##### Problem 3

6) 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

7) 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) $45^{\circ} \text{ }$b) $60^{\circ} \text{ }$c) $90^{\circ} \text{ }$d) $180^{\circ}$
##### Problem 5

8) 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

9) Lines ﻿$l$﻿ 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. Write each corresponding letter in the answer box and separate letters with commas.

a) A ﻿$\quad\quad$﻿ b) B ﻿$\quad\quad$﻿ c) C ﻿$\quad\quad$﻿ d) D ﻿$\quad\quad$﻿ e) E ##### Problem 7

Here is triangle ﻿$POG$﻿ followed by images of four rotations of ﻿$POG$﻿. Match each description below with one of the images. Write the number of the corresponding image in the answer box. 10) Rotate 60 degrees clockwise around O.

11) Rotate 120 degrees clockwise around O.

12) Rotate 60 degrees counterclockwise around O.

13) Rotate 60 degrees clockwise around P.