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. 1.

   Ari slides a robot sticker 5 units right. Side CD is 6 units long, and the table row is CD | C′D′ = 6 | ?. How long is C′D′?

   6

2. 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′ | ?

3. 2.

   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

4. 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′ | ?

5. 3.

   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
6. 4.

   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
7. 5.

   Side UV of Milo's house drawing goes from U(-4, 3) to V(-4, 8). Milo slides the drawing 2 units down. How long is U′V′, in units?

   5
8. 6.

   Side QS of Noah's ladder drawing goes from Q(1, 3) to S(1, 8). Noah slides the drawing 2 units up. How long is Q′S′, in units?

   5
9. 7.

   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

10. 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′ | ?

11. 8.

    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
12. 9.

    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
13. 10.

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