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8th grade Why a line has the same slope everywhere (similar triangles) worksheet

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Why a line has the same slope everywhere (similar triangles)

Grade 8 Math Worksheet

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

  1. Ren's ramp has a small slope triangle with run 8 feet and rise 3 feet. A bigger triangle on the same ramp has run 12 feet. What is its rise, in feet?

  2. Tala's sledding hill has a small slope triangle with run 7 feet and rise 4 feet. A bigger triangle on the same hill has rise 6 feet. What is its run, in feet?

  3. Ari's kite string slopes up. A small slope triangle has run 3 feet and rise 5 feet. A bigger triangle has rise 8 feet. What is its run, in feet?

  4. Esme's printer graph is a straight line from (0, 0). The slope triangle to the marked point has run 6 minutes and rise 9 pages. What is the rise at 14 minutes?

  5. Jun's scooter graph is a straight line from (0, 0). The slope triangle to the marked point has run 5 minutes and rise 3 blocks. What is the rise at 20 minutes?

  6. Two slope triangles are drawn for Kira's ramp. One has run 4 and rise 3. The other has run 12 and rise 9. Could both be slope triangles of one straight line?

    • No, the runs are different
    • No, the rises are different
    • Yes, both slopes are 3/4
    • Yes, the second rise is bigger

  7. Two slope triangles are drawn for Luz's sledding hill. One has run 6 and rise 4. The other has run 15 and rise 9. Could both be slope triangles of one straight line?

    • Yes, both slopes are about the same
    • No, the slopes are 2/3 and 3/5
    • No, the rises are different
    • Yes, the second triangle is just bigger

  8. Two slope triangles are drawn for Milo's roof line. One has run 6 and rise 10. The other has run 10 and rise 16. Could both be slope triangles of one straight line?

    • Yes, both slopes are about the same
    • No, the slopes are 5/3 and 8/5
    • No, the rises are different
    • Yes, the second triangle is just bigger

  9. A small and a large slope triangle sit under Tala's ramp, one above the other. Both have the same slope. Which reason is right?

    • The triangles are similar, so rise ÷ run is the same
    • The long sides are equal in length, so rise ÷ run is the same
    • The rises are equal, so rise ÷ run is the same
    • The runs are equal, so rise ÷ run is the same

  10. Zee draws two slope triangles of different sizes under a sledding hill's line. They share one angle at the bottom. Why is their rise ÷ run the same?

    • Both triangles have the same rise, so rise ÷ run is the same
    • Both triangles have the same long side, so rise ÷ run is the same
    • Equal angles make the triangles similar, so rise ÷ run is the same
    • Both triangles have the same area, so rise ÷ run is the same
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8th grade Why a line has the same slope everywhere (similar triangles) worksheet – printable
Print: 123456

About this worksheet

Slope from similar triangles. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can use a small slope triangle to find a missing rise or run on a bigger one, because both sit on the same line.
  • I can say why every slope triangle on a straight line gives the same slope, and I know a bigger triangle does not make the slope bigger.
  • I can write the rule y = mx for a line through (0, 0), and find a point on a line that starts above zero by scaling a triangle from a point I know.

Standard: 8.EE.B.6 (slope part)

Words to know

slope triangle: A right triangle under a line: its flat side is the run, its upright side is the rise.

similar triangles: Same shape, different size: both sides are multiplied by the same number.

scale factor: The number that turns the small triangle's sides into the big one's.

slope: The rise for each 1 of run. For any triangle on the line it is rise ÷ run.

y = mx: The rule for a line through (0, 0): y is the slope m times x.

Common mistakes

Your child added the same amount to both triangle sides instead of multiplying. Try it with a photo that is doubled: if a picture is 4 wide and 3 tall, how tall is the copy that is 8 wide?

Your child divided by the scale factor when the bigger triangle needs multiplying.

Your child kept the right numbers but swapped run and rise.

What to say

Ask: is the big triangle's side bigger or smaller than the small one's?

Ask: in a slope, which number goes on top, the rise or the run?

Questions parents ask

What is the most common mistake with why a line has the same slope everywhere (similar triangles)?

Your child added the same amount to both triangle sides instead of multiplying. Try it with a photo that is doubled: if a picture is 4 wide and 3 tall, how tall is the copy that is 8 wide?

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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