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.

   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
2. 2.

   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
3. 3.

   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
4. 4.

   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?

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

   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 rises are different
   • Yes, the second triangle is just bigger
   • No, the slopes are 5/3 and 8/5
6. 6.

   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
7. 7.

   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
8. 8.

   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
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 area, so rise ÷ run is the same
   • Equal angles make the triangles similar, so rise ÷ run is 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
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?

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