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.

   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
5. 5.

   Bo's snail graph is a straight line from (0, 0). The slope triangle to the marked point has run 4 minutes and rise 6 inches. What is the rise at 12 minutes?

   18
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.

   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?

   12
8. 8.

   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?

   • Yes, both slopes are 3/4
   • No, the rises are different
   • Yes, the second rise is bigger
   • No, the runs are different
9. 9.

   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 long side, so rise ÷ run is the same
   • Both triangles have the same rise, so rise ÷ run is the same
   • Both triangles have the same area, so rise ÷ run is the same
   • Equal angles make the triangles similar, so rise ÷ run is the same
10. 10.

    Ari measures two slope triangles on a roof line. One is twice as long and twice as tall as the other. Which reason explains the same slope?

    • The long side is doubled, so rise ÷ run does not change
    • Both legs are added to by 2, so rise ÷ run does not change
    • Only the run is doubled, so rise ÷ run does not change
    • Both legs are multiplied by 2, so rise ÷ run does not change