What stays the same? Rigid motions and congruent shapes

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The bus sticker with side FG marked and an arrow 4 units down; the image is not drawn. Table side | length: FG | 7; F′G′ | ?

2. 1.

   Bo slides a bus sticker 4 units down. Side FG is 7 units long, and the table row is FG | F′G′ = 7 | ?. How long is F′G′?

   7

3. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The castle sticker with side DH marked and an arrow 7 units left; the image is not drawn. Table side | length: DH | 5; D′H′ | ?

4. 2.

   Esme slides a castle sticker 7 units left. Side DH is 5 units long, and the table row is DH | D′H′ = 5 | ?. How long is D′H′?

   5
5. 3.

   Jun slides a rocket sticker 3 units up. Side CF is 8 units long, and the table row is CF | C′F′ = 8 | ?. How long is C′F′?

   8

6. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The kite drawing with C(-2, 1) and D(-2, 6) marked; the image is not drawn.

7. 4.

   Side CD of Kira's kite drawing goes from C(-2, 1) to D(-2, 6). Kira slides the drawing 4 units right. How long is C′D′, in units?

   5

8. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The star sticker with ∠H marked and a curved arrow 270° counterclockwise about the origin; the image is not drawn. Table angle | size: ∠H | 35°; ∠H′ | ?

9. 5.

   Zee turns a star sticker 270° counterclockwise about the origin. Angle H on the sticker is 35°, and the table row is ∠H | ∠H′ = 35° | ?. What is ∠H′, in degrees?

   35
10. 6.

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. Tala flips an umbrella sticker across the y-axis. Angle G on the sticker is 110°, and the table row is ∠G | ∠G′ = 110° | ?. What is ∠G′, in degrees?

    110
11. 7.

    D(4, 2) | D′(-2, 4); F(1, 5) | F′(-5, 1). Ari's table for a butterfly design: D(4, 2) → (-2, 4) and F(1, 5) → (-5, 1). Both rows fit (x, y) → (−y, x). Which move is it?

    • a flip across the y-axis
    • a dilation with scale factor 2 about the origin
    • a turn of 90° counterclockwise about the origin
    • a slide 6 units left and 2 units up
12. 8.

    D(2, 6) | D′(6, -2); F(5, 3) | F′(3, -5). Bo's table for a leaf design: D(2, 6) → (6, -2) and F(5, 3) → (3, -5). Both rows fit (x, y) → (y, −x). Which move is it?

    • a dilation with scale factor 2 about the origin
    • a turn of 90° clockwise about the origin
    • a flip across the x-axis
    • a slide 4 units right and 8 units down
13. 9.

    D(3, 4) | D′(3, -4); F(6, 1) | F′(6, -1). Esme's table for a quilt design: D(3, 4) → (3, -4) and F(6, 1) → (6, -1). Both rows fit (x, y) → (x, −y). Which move is it?

    • a dilation with scale factor 2 about the origin
    • a flip across the x-axis
    • a turn of 90° clockwise about the origin
    • a slide 8 units down
14. 10.

    D(-2, 5) | D′(2, 5); F(-6, 3) | F′(6, 3). Jun's table for a snowflake design: D(-2, 5) → (2, 5) and F(-6, 3) → (6, 3). Both rows fit (x, y) → (−x, y). Which move is it?

    • a dilation with scale factor 2 about the origin
    • a turn of 180° about the origin
    • a flip across the y-axis
    • a slide 4 units right