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 𝐡𝐷.

Q2:

What does (𝐴𝐢) equal to?

  • A(𝐢𝐷)Γ—(𝐢𝐡)
  • B(𝐴𝐷)Γ—(𝐢𝐷)
  • C𝐢𝐷×𝐷𝐡
  • D𝐢𝐷×𝐢𝐡

Q3:

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

  • A𝐡𝐷, 𝐢𝐷
  • B𝐡𝐷, 𝐡𝐢
  • C𝐢𝐷, 𝐡𝐢

Q4:

What does (𝐴𝐷) equal to?

  • A𝐢𝐷×𝐷𝐡
  • B𝐢𝐷×𝐢𝐡
  • C𝐢𝐡×𝐷𝐡
  • D𝐴𝐡×𝐴𝐢

Q5:

Fill in the blank: π‘₯𝑙=…𝑛.

  • A𝑦
  • Bπ‘₯
  • Cπ‘š
  • D𝑧

Q6:

From the figure, determine the length of 𝐡𝐷. 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 𝐡𝐷.

Q10:

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

Q11:

From the figure shown, if 𝑋𝐿=40, and π‘ŒπΏ=30, what is π‘Œπ‘?

Q12:

Given that 𝐴𝐷=25, find 𝐹𝐡.

Q13:

Find the length of 𝐴𝐡.

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

Q14:

Given that the area of the trapezoid 𝐴𝐡𝐢𝐷 is 9,522 cm2, determine the length of 𝐡𝐹.

Q15:

Calculate the length of 𝐴𝐢.

Q16:

What does (𝐴𝐢) equal to?

  • A𝐴𝐷+𝐢𝐷
  • B𝐴𝐡+𝐢𝐡
  • C(𝐴𝐷)+(𝐢𝐷)
  • D(𝐴𝐡)+(𝐢𝐡)

Q17:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐴𝐡?

  • A𝐴𝐡
  • B𝐡𝐷
  • C𝐡𝐢

Q18:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐡𝐢?

  • A𝐴𝐡
  • B𝐡𝐢
  • C𝐡𝐷

Q19:

𝐴𝐷=⋯×𝐢𝐴𝐢𝐡.

  • A𝐢𝐷
  • B𝐡𝐷
  • C𝐴𝐡

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?

  • A𝐷𝐡, 𝐡𝐢
  • B𝐴𝐡, 𝐴𝐢
  • C𝐷𝐡, 𝐷𝐢

Q22:

Which segment is the altitude of △𝐴𝐡𝐢?

  • A𝐡𝐷
  • B𝐢𝐷
  • C𝐴𝐷
  • D𝐡𝐢
  • E𝐴𝐡

Q23:

Find the base of the altitude 𝐢𝐷 in △𝐴𝐡𝐢.

  • A𝐡𝐷
  • B𝐴𝐡
  • C𝐴𝐷

Q24:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐴𝐢?

  • A𝐡𝐷
  • B𝐴𝐡
  • C𝐡𝐢

Q25:

In the figure below, 𝐢∈𝐡𝐷, π‘šβˆ π΅=π‘šβˆ π·=90∘, π‘šβˆ πΆπΈπ·=30∘, π‘šβˆ π΄πΈπΆ=45∘, π‘šβˆ π΅π΄πΆ=60∘, and 𝐢𝐷=8cm. Find the length of 𝐴𝐢.

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

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