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8th grade What stays the same? Rigid motions and congruent shapes worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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What stays the same? Rigid motions and congruent shapes

Grade 8 Math Worksheet - Building Confidence

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

  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′?

  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. 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′?

  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′?

  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. 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?

  7. 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?

  8. 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?

  9. 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?

  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. 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?

  12. 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. 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
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8th grade What stays the same? Rigid motions and congruent shapes worksheet – printable
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About this worksheet

What stays the same? Rigid motions and congruent shapes. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can say that a slide, flip or turn keeps every length, every angle and parallel sides, and that a dilation changes the lengths.
  • I can name the single move from a shape and its image, and pick the two moves, in order, that take one shape onto a congruent one.
  • I can tell when the corners still go around the same way (slides and turns) and when they reverse (flips).

Standard: 8.G.A.1a–c, 8.G.A.2

Words to know

rigid motion: A slide, flip or turn: the shape moves but keeps its size and shape.

congruent: Same shape and same size; one fits exactly on the other.

preimage / image: The shape before a move / the shape after it (D becomes D′).

parallel: Lines that stay the same distance apart and never meet.

orientation: Which way the corners go around: clockwise or counterclockwise.

dilation: Enlarging or shrinking from a point; it keeps shape but changes size.

Common mistakes

Your child added the size of the slide to the length of a side, as if sliding stretched the shape. Slide a ruler across the table together: does it get longer?

Your child added the two coordinates instead of finding the distance between them. Count the squares between the two points on graph paper together.

Your child added the size of the turn to the angle, as if turning a shape opened its corners wider. Turn a book a quarter turn: are its corners still square?

Questions parents ask

What is the most common mistake with what stays the same? rigid motions and congruent shapes?

Your child added the size of the slide to the length of a side, as if sliding stretched the shape. Slide a ruler across the table together: does it get longer?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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