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

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What stays the same? Rigid motions and congruent shapes

Grade 8 Math Worksheet - Challenge Me

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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 sticker and its final image are both drawn, with D, D′, F and F′ labeled; the middle step is not drawn.

  2. Luz's rocket sticker moved twice. Corner D went from (2, 1) to (1, 1), and F went from (4, 5) to (-1, 5). Which moves, in order, did it?

    • a slide 1 unit left
    • a flip across the y-axis, then a slide 3 units right
    • a turn of 180° about the origin, then a slide 3 units right
    • a slide 3 units right, then a flip across the y-axis

  3. Noah's boat sticker moved twice. Corner D went from (2, 3) to (2, -1), and F went from (6, 4) to (6, -2). Which moves, in order, did it?

    • a flip across the y-axis, then a slide 2 units up
    • a slide 2 units up, then a flip across the x-axis
    • a slide 4 units down
    • a flip across the x-axis, then a slide 2 units up

  4. Pia's car sticker moved twice. Corner D went from (1, 2) to (4, -2), and F went from (3, -1) to (2, 1). Which moves, in order, did it?

    • a flip across the x-axis, then a slide 5 units right
    • a slide 5 units right, then a turn of 180° about the origin
    • a slide 3 units right and 4 units down
    • a turn of 180° about the origin, then a slide 5 units right

  5. On Ren's tent sticker, C is 6 units straight above D. After a half turn (180°) about the origin, D′ is at (4, 1). Where is C′? Write it like (7, -3).

  6. On Ari's leaf sticker, C is 3 units to the right of D. After a flip across the y-axis, D′ is at (-4, 6). Where is C′? Write it like (7, -3).

  7. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The sticker with C, D and F labeled and a curved arrow showing clockwise; the image is not drawn.

  8. On Esme's star sticker, corners C, D and F go around clockwise. Esme flips the sticker across the y-axis. Which way do C′, D′ and F′ go around?

    • clockwise, the same way as before
    • it depends on how far the sticker moves
    • counterclockwise, the other way

  9. On Kira's snowman sticker, corners C, D and F go around clockwise. Kira flips the sticker across the x-axis. Which way do C′, D′ and F′ go around?

    • it depends on how far the sticker moves
    • counterclockwise, the other way
    • clockwise, the same way as before

  10. neither image is drawn. Side DF of Milo's castle picture is 4 units long. Milo dilates it with scale factor 3 about the origin, then slides it 2 units right. How long is D′F′?

  11. Side DF of Noah's house picture is 7 units long. Noah slides it 4 units up, then dilates it with scale factor 2 about the origin. How long is D′F′?

  12. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Side DF of the car picture is marked; neither image is drawn.

  13. Side DF of Ren's car picture is 6 units long. Ren turns it 180° about the origin, then slides it 5 units left. How long is D′F′?

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8th grade What stays the same? Rigid motions and congruent shapes worksheet – printable
Print: 123456

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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