The altitude of a right triangle: three similar triangles and the geometric mean

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Tala glues a strip from the square corner of a triangle window to the long edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is HF, in inches?

   36/5
2. 2.

   Ari folds a paper right triangle from the square corner to the long edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is HF, in cm?

   18
3. 3.

   Bo props a pole from the square corner of a tent side to the slanted edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is CH, in feet?

   12
4. 4.

   Esme cuts a triangle sandwich from the square corner to the long edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is CH, in inches?

   24/5
5. 5.

   Jun plans a path from the square corner of a park to the far edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is CH, in meters?

   36/5
6. 6.

   Kira glues a strip from the square corner of a triangle window to the long edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is CH, in inches?

   48/5
7. 7.

   Luz adds a support from the square corner of a ramp to its slope. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is DF, in feet?

   18
8. 8.

   Milo cuts a wedge of cheese from the square corner to the long edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is DF, in inches?

   28
9. 9.

   Noah plans a path from the square corner of a park to the far edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is DF, in meters?

   45
10. 10.

    Pia folds a paper right triangle from the square corner to the long edge. In right △DCF, the right angle is at C, and CH ⊥ DF. How long is DF, in cm?

    25