Worksheet: Right Triangle Altitude Theorem

In this worksheet, we will practice using the right triangle altitude theorem to find a missing length.

Q1:

Find the length of 𝐵 𝐷 .

Q2:

What does ( 𝐴 𝐶 ) 2 equal to?

  • A ( 𝐶 𝐷 ) × ( 𝐶 𝐵 ) 2 2
  • B ( 𝐴 𝐷 ) × ( 𝐶 𝐷 ) 2 2
  • C 𝐶 𝐷 × 𝐷 𝐵
  • D 𝐶 𝐷 × 𝐶 𝐵

Q3:

In the given figure, ( 𝐴 𝐵 ) 2 is equal to the product of which two other lengths?

  • A 𝐵 𝐷 , 𝐶 𝐷
  • B 𝐶 𝐷 , 𝐵 𝐶
  • C 𝐵 𝐷 , 𝐵 𝐶

Q4:

What does ( 𝐴 𝐷 ) 2 equal to?

  • A 𝐶 𝐵 × 𝐷 𝐵
  • B 𝐶 𝐷 × 𝐶 𝐵
  • C 𝐴 𝐵 × 𝐴 𝐶
  • D 𝐶 𝐷 × 𝐷 𝐵

Q5:

Fill in the blank: 𝑥 𝑙 = 𝑛 .

  • A 𝑧
  • B 𝑥
  • C 𝑚
  • D 𝑦

Q6:

From the figure, determine the length of 𝐵 𝐷 . If necessary, round your answer to the nearest hundredth.

Q7:

Determine the length of 𝐴 𝐷 .

Q8:

In the following figure, find the length of 𝑃 𝑆 .

Q9:

Find the length of 𝐵 𝐷 .

Q10:

Find the length of 𝐴 𝐹 approximating the result to the nearest hundredth.

Q11:

From the figure shown, if 𝑋 𝐿 = 4 0 , and 𝑌 𝐿 = 3 0 , what is 𝑌 𝑍 ?

Q12:

Given that 𝐴 𝐷 = 2 5 , find 𝐹 𝐵 .

Q13:

Find the length of 𝐴 𝐵 .

Q14:

Given that the area of the trapezium 𝐴 𝐵 𝐶 𝐷 is 9,522 cm2, determine the length of 𝐵 𝐹 .

Q15:

Calculate the length of 𝐴 𝐶 .

Q16:

What does ( 𝐴 𝐶 ) 2 equal to?

  • A 𝐴 𝐷 + 𝐶 𝐷
  • B ( 𝐴 𝐵 ) + ( 𝐶 𝐵 ) 2 2
  • C 𝐴 𝐵 + 𝐶 𝐵
  • D ( 𝐴 𝐷 ) + ( 𝐶 𝐷 ) 2 2

Q17:

Which line segment is the altitude of triangle 𝐴 𝐵 𝐶 which is perpendicular to 𝐴 𝐵 ?

  • A 𝐴 𝐵
  • B 𝐵 𝐷
  • C 𝐵 𝐶

Q18:

Which line segment is the altitude of triangle 𝐴 𝐵 𝐶 which is perpendicular to 𝐵 𝐶 ?

  • A 𝐵 𝐶
  • B 𝐵 𝐷
  • C 𝐴 𝐵

Q19:

𝐴 𝐷 = × 𝐶 𝐴 𝐶 𝐵 .

  • A 𝐶 𝐷
  • B 𝐵 𝐷
  • C 𝐴 𝐵

Q20:

In the figure below, find the length of 𝑋 𝐸 .

Q21:

In the given figure, ( 𝐷 𝐴 ) 2 is equal to the product of which two other lengths?

  • A 𝐷 𝐵 , 𝐵 𝐶
  • B 𝐴 𝐵 , 𝐴 𝐶
  • C 𝐷 𝐵 , 𝐷 𝐶

Q22:

Which segment is the altitude of 𝐴 𝐵 𝐶 ?

  • A 𝐵 𝐷
  • B 𝐴 𝐷
  • C 𝐴 𝐵
  • D 𝐶 𝐷
  • E 𝐵 𝐶

Q23:

Find the base of the altitude 𝐶 𝐷 in 𝐴 𝐵 𝐶 .

  • A 𝐵 𝐷
  • B 𝐴 𝐷
  • C 𝐴 𝐵

Q24:

Which line segment is the altitude of triangle 𝐴 𝐵 𝐶 which is perpendicular to 𝐴 𝐶 ?

  • A 𝐴 𝐵
  • B 𝐵 𝐶
  • C 𝐵 𝐷

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