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.

   Jun's toy ramp rests on a stack of books. Points A and B are marked on its side view. How high is the ramp at C, 16 inches across?

   14
3. 3.

   Kira starts a bike ride some miles from home at a steady speed. Points A and B are marked. How many miles from home is Kira at C, after 5 hours?

   32
4. 4.

   Luz's sunflower grows at a steady rate. Points A and B are marked on its height graph. On which day, at C, is it 35 inches tall?

   22
5. 5.

   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
6. 6.

   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
7. 7.

   Zee's snail graph is a straight line through (0, 0). Its slope triangle has run 3/4 minute and rise 5/6 inch. What rule gives y (inches) for any x (minutes)?

   y = 10x ÷ 9
8. 8.

   The given slope triangle on Esme's roof has run 8 inches and rise 5 inches. A smaller triangle on the roof is half the size of the given one. What is the roof's slope?

   5/8
9. 9.

   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
10. 10.

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

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