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

Answer Key - Grade 8 Math Worksheet

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

1. 1.

   Noah's sledding hill has a small slope triangle with run 4 feet and rise 3 feet. A bigger triangle on the same hill has run 10 feet. What is its rise, in feet?

   7 1/2
2. 2.

   A small slope triangle on Pia's roof has run 6 inches and rise 5 inches. A bigger triangle on the same roof has run 15 inches. What is its rise, in inches?

   12 1/2
3. 3.

   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?

   4 1/2
4. 4.

   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?

   10 1/2
5. 5.

   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 4/5
6. 6.

   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?

   21
7. 7.

   Noah's snail graph is a straight line through (0, 0). Its slope triangle has run 6 minutes and rise 4 inches. What rule gives y (inches) for any x (minutes)?

   y = 2x ÷ 3
8. 8.

   Pia's printer graph is a straight line through (0, 0). Its slope triangle has run 8 minutes and rise 10 pages. What rule gives y (pages) for any x (minutes)?

   y = 5x ÷ 4
9. 9.

   Ren's sunflower graph is a straight line through (0, 0). Its slope triangle has run 12 days and rise 9 inches. What rule gives y (inches) for any x (days)?

   y = 3x ÷ 4
10. 10.

    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