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 castle sticker with side DH marked and an arrow 7 units left; the image is not drawn. Table side | length: DH | 5; D′H′ | ?

2. 1.

   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
3. 2.

   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
4. 3.

   Side FG of Luz's tent drawing goes from F(3, 2) to G(3, 9). Luz slides the drawing 5 units left. How long is F′G′, in units?

   7
5. 4.

   Pia turns a kite sticker 90° counterclockwise about the origin. Angle D on the sticker is 48°, and the table row is ∠D | ∠D′ = 48° | ?. What is ∠D′, in degrees?

   48

6. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The boat sticker with ∠F marked and a curved arrow 180° about the origin; the image is not drawn. Table angle | size: ∠F | 65°; ∠F′ | ?

7. 5.

   Ren turns a boat sticker 180° about the origin. Angle F on the sticker is 65°, and the table row is ∠F | ∠F′ = 65° | ?. What is ∠F′, in degrees?

   65

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. 6.

   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. 7.

    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. 8.

    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. 9.

    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 turn of 90° clockwise about the origin
    • a flip across the x-axis
    • a dilation with scale factor 2 about the origin
    • a slide 4 units right and 8 units down
13. 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 turn of 180° about the origin
    • a flip across the y-axis
    • a dilation with scale factor 2 about the origin
    • a slide 4 units right