Worksheet

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

Grade 10 Math Worksheet - Building Confidence

NameDate

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

  1. Ren 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 CH, in feet?

  2. Tala 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?

  3. Zee 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?

  4. Ari 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?

  6. Bo 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. Which proportion is true?

    • DH : CH = CH : HF
    • DH : HF = CH : CD
    • DH : CH = CH : DF
    • DH : CH = HF : CH

  7. Esme 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. Which proportion is true?

    Use the picture in question 5.

    • DH : CD = DF : CD
    • DH : CD = CD : DF
    • HF : CD = CD : DF
    • CD : DH = DF : CF

  8. Jun 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. Which proportion is true?

    Use the picture in question 5.

    • CF : HF = DF : CD
    • DH : CF = CF : DF
    • HF : CF = CF : DF
    • HF : CF = DF : CF

  9. Kira draws a road from the square corner of a triangle of streets to the long street. In right △DCF, the right angle is at C, and CH ⊥ DF. Which proportion is true?

    Use the picture in question 5.

    • CH : HF = CD : DF
    • CH : DH = CH : HF
    • CH : DH = DF : CH
    • CH : DH = HF : CH

  10. Milo 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 CD, in inches?

  11. 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 CD, in meters?

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

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

  1. Ren 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 CH, in feet?

    10

  2. Tala 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?

    8

  3. Zee 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?

    6

  4. Ari 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?

    8

  6. Bo 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. Which proportion is true?

    • DH : CH = CH : HF
    • DH : HF = CH : CD
    • DH : CH = CH : DF
    • DH : CH = HF : CH

  7. Esme 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. Which proportion is true?

    Use the picture in question 5.

    • DH : CD = DF : CD
    • DH : CD = CD : DF
    • HF : CD = CD : DF
    • CD : DH = DF : CF

  8. Jun 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. Which proportion is true?

    Use the picture in question 5.

    • CF : HF = DF : CD
    • DH : CF = CF : DF
    • HF : CF = CF : DF
    • HF : CF = DF : CF

  9. Kira draws a road from the square corner of a triangle of streets to the long street. In right △DCF, the right angle is at C, and CH ⊥ DF. Which proportion is true?

    Use the picture in question 5.

    • CH : HF = CD : DF
    • CH : DH = CH : HF
    • CH : DH = DF : CH
    • CH : DH = HF : CH

  10. Milo 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 CD, in inches?

    12

  11. 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 CD, in meters?

    10