The Triangle Proportionality (side-splitting) Theorem

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Milo builds a ramp with a brace GH. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is HF, in feet?

   12
2. 2.

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

   10
3. 3.

   Ren fixes a crossbar GH across a tent front. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is HF, in feet?

   21
5. 4.

   Tala cuts a wedge of cheese along GH. In △CDF, GH ∥ DF, with G on CD and H on CF. Which proportion is true?

   • CG : GD = CH : HF
   • CG : GD = HF : CH
   • CG : GD = GH : DF
   • CG : CD = CH : HF
6. 5.

   Zee slices a triangle sandwich along GH. In △CDF, GH ∥ DF, with G on CD and H on CF. Which proportion is true?

   Use the picture in question 4.

   • GD : CG = CH : HF
   • GD : CD = HF : CH
   • GD : CG = DF : GH
   • GD : CG = HF : CH
7. 6.

   Ari glues a wooden strip GH across a triangle window. In △CDF, GH ∥ DF, with G on CD and H on CF. Which proportion is true?

   Use the picture in question 4.

   • CD : CG = CH : CF
   • CG : CD = CH : HF
   • CG : GD = GH : DF
   • CG : CD = CH : CF
8. 7.

   Bo cuts a straight line GH across a pizza slice. In △CDF, GH ∥ DF, with G on CD and H on CF. Which proportion is true?

   Use the picture in question 4.

   • CG : GD = CD : CF
   • CG : GD = GH : DF
   • CG : CD = GH : DF
   • CG : CD = DF : GH
9. 8.

   Jun walks a path GH across a triangle park. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is CH, in feet?

   4
10. 9.

    Kira folds a paper triangle along GH. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is CH, in inches?

    9
11. 10.

    Luz looks at a stepladder with a spreader bar GH. In △CDF, GH ∥ DF, with G on CD and H on CF. How long is CH, in feet?

    5