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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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

Grade 8 Math Worksheet - Building Confidence

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

  1. Read this first

    Ratio table (run | rise)

    Small triangle 8 | 3, large triangle 40 | ?, with the arrow × 5 beside both columns. Run and rise in feet.

  2. A small slope triangle on Kira's sledding hill has run 8 feet and rise 3 feet. The bigger triangle has run 40 feet (arrow × 5). What is its rise, in feet?

  3. Ratio table (run | rise)

    Small triangle 2 | 5, large triangle 4 | ?, with the arrow × 2 beside both columns. Run and rise in feet.

  4. Luz's kite string slopes up. A small slope triangle has run 2 feet and rise 5 feet. The bigger triangle has run 4 feet (arrow × 2). What is its rise, in feet?

  5. Ratio table (run | rise)

    Small triangle 6 | 3, large triangle 18 | ?, with the arrow × 3 beside both columns. Run and rise in feet.

  6. A small slope triangle on Milo's roof has run 6 feet and rise 3 feet. The bigger triangle has run 18 feet (arrow × 3). What is its rise, in feet?

  7. Pia's sledding hill has a small slope triangle with run 10 feet and rise 3 feet. A bigger triangle on the same hill has run 30 feet. What is its rise, in feet?

  8. A small slope triangle on Ren's roof has run 12 inches and rise 5 inches. A bigger triangle on the same roof has run 36 inches. What is its rise, in inches?

  9. A rope slopes up to Tala's tent top. A small slope triangle has run 3 feet, rise 4 feet. A bigger one has run 6 feet. What is its rise, in feet?

  10. Zee's sledding hill has a small slope triangle with run 8 feet and rise 3 feet. A bigger triangle on the same hill has rise 9 feet. What is its run, in feet?

  11. A small slope triangle on Jun's ramp has run 24 inches and rise 2 inches. A bigger triangle on the same ramp is 3 times as big. What is the slope of the ramp?

  12. A small slope triangle on Luz's sledding hill has run 8 feet and rise 3 feet. A bigger triangle on the same hill is 4 times as big. What is the slope of the hill?

  13. Milo's kite string slopes up. A small slope triangle has run 2 feet and rise 5 feet. A bigger triangle is 3 times as big. What is the slope of the string?

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