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

3. 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
4. 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

5. 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.

6. 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
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 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′ | ?

11. 8.

    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
12. 9.

    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 slide 6 units left and 2 units up
    • a dilation with scale factor 2 about the origin
    • a flip across the y-axis
    • a turn of 90° counterclockwise about the origin
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 slide 4 units right
    • a flip across the y-axis
    • a dilation with scale factor 2 about the origin