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.

   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
4. 4.

   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
5. 5.

   Ren's roof has slope 5/12. A slope triangle under it has run 9 feet. What is its rise, in feet?

   3 3/4
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.

   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
8. 8.

   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
9. 9.

   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
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: a longer triangle rises more, so its slope is bigger
    • 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