The Triangle Proportionality (side-splitting) Theorem

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Noah adds a beam GH to a roof front. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is HF, in feet?

   12
2. 2.

   Ren sews a seam GH across a sail. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is HF, in inches?

   9
3. 3.

   Tala builds a ramp with a brace GH. In △CDF, GH ∥ DF, with G on CD and H on CF. What is x?

   5
4. 4.

   Zee maps a road GH across a triangle of streets. In △CDF, GH ∥ DF, with G on CD and H on CF. What is x?

   6
5. 5.

   Ari cuts a wedge of cheese along GH. In △CDF, GH ∥ DF, with G on CD and H on CF. What is x?

   7
6. 6.

   Bo glues a strip GH across a triangle window. In △CDF, GH ∥ DF, with G on CD and H on CF. What is x?

   9
7. 7.

   Esme checks whether a tent's crossbar GH is level with the ground DF. G is on CD and H is on CF. Is GH ∥ DF?

   • No: the gaps 2 and 3 are different
   • Yes: 6/4 = 9/6 = 3/2
   • Not enough: GH and DF are needed
   • No: CG = 4 but CH = 6
8. 8.

   Jun checks whether a ramp brace GH runs beside the ground DF. G is on CD and H is on CF. Is GH ∥ DF?

   • Not enough: GH and DF are needed
   • Yes: 7/5 and 9/7 both put the bottom piece on top
   • No: 7/5 but 9/7
   • Yes: both bottom pieces are 2 longer
9. 9.

   Kira checks whether a ladder's spreader bar GH runs beside the floor DF. G is on CD and H is on CF. Is GH ∥ DF?

   • No: the gaps 3 and 4 are different
   • Not enough: GH and DF are needed
   • Yes: 6/3 = 8/4 = 2
   • No: CG = 3 but CH = 4
10. 10.

    Luz checks whether a roof beam GH runs beside the ceiling DF. G is on CD and H is on CF. Is GH ∥ DF?

    • Yes: 6/4 and 8/6 both put the bottom piece on top
    • Yes: both bottom pieces are 2 longer
    • Not enough: GH and DF are needed
    • No: 6/4 = 3/2 but 8/6 = 4/3