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 𝐵𝐷.

Q2:

What does (𝐴𝐶) equal to?

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

Q3:

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

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

Q4:

What does (𝐴𝐷) equal to?

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

Q5:

Fill in the blank: 𝑥𝑙=𝑛.

  • A 𝑦
  • B 𝑥
  • C 𝑚
  • D 𝑧

Q6:

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

Q7:

Determine the length of 𝐴𝐷.

  • A7.55 cm
  • B8.9 cm
  • C6.87 cm
  • D4 cm

Q8:

In the following figure, find the length of 𝑃𝑆.

Q9:

Find the length of 𝐵𝐷.

Q10:

Find the length of 𝐴𝐹 approximating the result to the nearest hundredth.

Q11:

From the figure shown, if 𝑋𝐿=40, and 𝑌𝐿=30, what is 𝑌𝑍?

Q12:

Given that 𝐴𝐷=25, find 𝐹𝐵.

Q13:

Find the length of 𝐴𝐵.

  • A15 cm
  • B9 cm
  • C7.2 cm
  • D12 cm

Q14:

Given that the area of the trapezium 𝐴𝐵𝐶𝐷 is 9,522 cm2, determine the length of 𝐵𝐹.

Q15:

Calculate the length of 𝐴𝐶.

  • A 8.8 cm
  • B 3.81 cm
  • C 4.4 cm
  • D 7.62 cm

Q16:

What does (𝐴𝐶) equal to?

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

Q17:

Which line segment is the altitude of triangle 𝐴𝐵𝐶 which is perpendicular to 𝐴𝐵?

  • A 𝐴 𝐵
  • B 𝐵 𝐷
  • C 𝐵 𝐶

Q18:

Which line segment is the altitude of triangle 𝐴𝐵𝐶 which is perpendicular to 𝐵𝐶?

  • A 𝐴 𝐵
  • B 𝐵 𝐶
  • C 𝐵 𝐷

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 𝑋𝐸.

Q21:

In the given figure, (𝐷𝐴) 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 𝐴𝐵𝐶?

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

Q23:

Find the base of the altitude 𝐶𝐷 in 𝐴𝐵𝐶.

  • A 𝐵 𝐷
  • B 𝐴 𝐵
  • C 𝐴 𝐷

Q24:

Which line segment is the altitude of triangle 𝐴𝐵𝐶 which is perpendicular to 𝐴𝐶?

  • A 𝐵 𝐷
  • B 𝐴 𝐵
  • C 𝐵 𝐶

Q25:

In the figure below, 𝐶𝐵𝐷, 𝑚𝐵=𝑚𝐷=90, 𝑚𝐶𝐸𝐷=30, 𝑚𝐴𝐸𝐶=45, 𝑚𝐵𝐴𝐶=60, and 𝐶𝐷=8cm. Find the length of 𝐴𝐶.

  • A16 cm
  • B12 cm
  • C24 cm
  • D15 cm

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