Unit 1, Lesson 15

Symmetry

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Integrated Math 1

Practice

Problem 1

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

<p>A flag. A blue background with a white X.</p>

<p>A triskelion image, three congruent legs radiating from a center point.</p>

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

ForLesson 14: Defining Rotations

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

<p>The letter Z, formed by 3 line segments. 4 points on the endpoints of the segments. Starting at the top left, A. Moving to the right, B. Slanting down and to the left, C. Moving to the right, D.</p>

Problem 4

ForLesson 14: Defining Rotations

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

$45^\circ$
$60^\circ$
$90^\circ$
$180^\circ$

Problem 5

ForLesson 9: Speedy Delivery

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

ForLesson 11: Defining Reflections

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.

<p>Perpendicular lines L and M.</p> — $m \perp \ell$

A
B
C
D
E

Problem 7

ForLesson 13: Incorporating Rotations

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

<p>Triangle P O G on isometric grid. P O and O G are both 2 units long. O G is vertical.</p>

Rotate 60 degrees clockwise around $O$.
Rotate 120 degrees clockwise around $O$.
Rotate 60 degrees counterclockwise around $O$.
Rotate 60 degrees clockwise around $P$.

Triangle P prime O prime G prime on an isometric grid. Point O prime faces downwards and to the left, P prime faces upwards, G prime faces downwards and to the right.
Triangle P prime O prime G prime on an isometric grid. Point O prime faces upwards and to the right, P prime faces downwards, G prime faces upwards and to the left.

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