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

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Bo's sunflower grows at a steady rate and was already tall at day 2. Points A and B are marked. How tall is it at C, on day 10?

   17
2. 2.

   Esme's tub already holds water when the circle runs at a steady rate. Points A and B are marked. How many gallons are in the tub at C, at 9 minutes?

   31
3. 3.

   Milo's tub already holds some water when the circle runs at a steady rate. Points A and B are marked on the graph. At what time, at point C, does the tub hold 24 gallons?

   11
4. 4.

   Noah starts a hike some miles from home at a steady pace. Points A and B are marked. After how many hours, at C, is Noah 28 miles from home?

   13
5. 5.

   Tala's sledding hill has slope 0.4. A slope triangle under it has run 6.5 meters. What is its rise, in meters?

   2.6
6. 6.

   Ari's measuring cup fills at a steady rate. Its slope triangle has run 1/2 minute and rise 3/4 cup. What rule gives y (cups) for any x (minutes)?

   y = 3x ÷ 2
7. 7.

   A slope triangle on Jun's sledding hill has run 10 feet and rise 3 feet. A bigger triangle on the same hill is 3/2 times as big. What is the slope of the hill?

   3/10
8. 8.

   Kira's kite string slopes up. A slope triangle has run 6 feet and rise 5 feet. A bigger triangle is 5/2 times as big. What is the slope of the string?

   5/6
9. 9.

   Luz says: "A longer slope triangle on the same ramp has a bigger slope." Which reply is right?

   • Yes: the slope is bigger near the top of the ramp
   • Yes: a longer triangle rises more, so its slope is bigger
   • No: the slope is the same because the long sides match each other along the ramp
   • No: all slope triangles on the ramp are similar, so rise ÷ run is the same
10. 10.

    Noah says: "A roof line has a steeper slope near the peak than near the edge." Which reply is right?

    • Yes: triangles near the peak are bigger, so their slope is bigger
    • No: slope triangles anywhere on a straight line are similar, so the slope is the same
    • Yes: the line bends upward toward the peak, so the slope grows
    • No: the slope is the same because every triangle has the same rise