Worksheet: Medians and Altitudes of Triangles

In this worksheet, we will practice identifying and using medians and altitudes of triangles.

Q1:

In β–³ 𝑋 π‘Œ 𝑍 , where 𝐴 is the midpoint of 𝑋 π‘Œ , what name is given to 𝐴 𝑍 ?

  • A hypotenuse
  • B base
  • C height
  • D median

Q2:

In a triangle 𝐴 𝐡 𝐢 , 𝑀 is the point of concurrency of its medians. If 𝐴 𝐷 is a median, then 𝐴 𝑀 = 𝑀 𝐷 .

  • A 2 3
  • B 1 2
  • C 1 3
  • D2

Q3:

What is length 𝑀 𝐡 rounded to the nearest hundredth?

Q4:

Find the length 𝐴 𝑀 , given that 𝐴 𝐸 = 5 4 .

Q5:

Determine the lengths of 𝐡 𝐷 and 𝐴 𝐡 .

  • A 𝐡 𝐷 = 1 2 . 2 5 c m , 𝐴 𝐡 = 2 4 . 5 c m
  • B 𝐡 𝐷 = 1 2 . 2 5 c m , 𝐴 𝐡 = 1 2 . 2 5 c m
  • C 𝐡 𝐷 = 2 8 . 5 c m , 𝐴 𝐡 = 2 8 . 5 c m
  • D 𝐡 𝐷 = 2 4 . 5 c m , 𝐴 𝐡 = 2 4 . 5 c m

Q6:

In β–³ 𝐽 𝐾 𝐿 , 𝑅 𝑃 = 2 . 1 c m . Find the length of 𝑃 𝐿 .

Q7:

In β–³ 𝐾 𝑀 𝐻 , 𝐾 𝑄 = 2 and 𝑄 𝑃 = ( 5 π‘₯ βˆ’ 7 ) . Find π‘₯ .

Q8:

In the given figure, segments 𝐴 𝐷 and 𝐢 𝐸 are the medians of β–³ 𝐴 𝐢 𝐡 , where 𝐴 𝐷 βŸ‚ 𝐢 𝐸 , 𝐴 𝐡 = 1 7 . 7 c m , and 𝐢 𝐸 = 9 c m . Determine 𝐢 𝐴 to the nearest tenth.

Q9:

In β–³ 𝐽 𝐾 𝐿 , 𝐽 𝑃 = 6 c m . Find the length of 𝑃 𝑆 .

Q10:

Given that the area of β–³ 𝐴 𝐸 𝐢 = 2 5 5 c m  , find the area of β–³ 𝐴 𝐡 𝐢 .

Q11:

Find the length of 𝐡 𝐷 and the perimeter of β–³ 𝐴 𝐡 𝐷 .

  • A 𝐡 𝐷 = 2 . 2 5 c m , perimeter of β–³ 𝐴 𝐡 𝐷 = 1 5 c m
  • B 𝐡 𝐷 = 9 c m , perimeter of β–³ 𝐴 𝐡 𝐷 = 1 8 c m
  • C 𝐡 𝐷 = 4 . 5 c m , perimeter of β–³ 𝐴 𝐡 𝐷 = 1 5 c m
  • D 𝐡 𝐷 = 4 . 5 c m , perimeter of β–³ 𝐴 𝐡 𝐷 = 1 3 . 5 c m

Q12:

Equilateral triangle 𝐴 𝐡 𝐢 has side 50.6. Given that 𝑀 is the intersection of its medians, determine οƒ  𝑀 𝐡 β‹… οƒ  𝐢 𝑀 .

Q13:

Given that 𝑃 𝐾 is a median of β–³ 𝐽 𝐿 𝑃 , 𝐽 𝐾 = 3 𝑦 βˆ’ 8 , and 𝐿 𝐾 = 2 𝑦 βˆ’ 4 , find the length of 𝐿 𝐾 .

Q14:

Use the data in the figure to determine the length of 𝐷 𝐹 and then the perimeter of β–³ 𝐷 𝐸 𝐹 .

  • A length of 𝐷 𝐹 = 1 8 c m , perimeter of β–³ 𝐷 𝐸 𝐹 = 8 8 c m
  • B length of 𝐷 𝐹 = 2 2 c m , perimeter of β–³ 𝐷 𝐸 𝐹 = 1 3 1 c m
  • C length of 𝐷 𝐹 = 3 0 c m , perimeter of β–³ 𝐷 𝐸 𝐹 = 9 0 c m
  • D length of 𝐷 𝐹 = 2 4 . 5 c m , perimeter of β–³ 𝐷 𝐸 𝐹 = 6 5 . 5 c m

Q15:

In triangle 𝐴 𝐡 𝐢 , 𝐴 𝐡 = 𝐴 𝐢 = 1 0 c m , 𝐡 𝐢 = 1 2 c m and 𝐷 is the midpoint of 𝐡 𝐢 . Find the length of 𝐴 𝐷 .

Q16:

In triangle 𝐴 𝐡 𝐢 , 𝐴 𝐡 = 𝐴 𝐢 = 1 0 c m , 𝐡 𝐢 = 1 6 c m and 𝐷 is the midpoint of 𝐡 𝐢 . Find the length of 𝐴 𝐷 .

Q17:

Given that 𝐴 𝐷 = 9 c m and 𝐸 𝐡 = 𝐴 𝐡 , find the perimeter of β–³ 𝑀 𝐷 𝐸 .

Q18:

Given that 𝐴 𝐡 = 𝐴 𝐢 = 2 2 c m , 𝐢 𝐡 = 2 0 c m , and 𝐸 𝐡 = 𝐸 𝐢 , find the length of 𝐴 𝐷 .

  • A 12 cm
  • B √ 2 cm
  • C 21 cm
  • D 8 √ 6 cm

Q19:

What is the length of 𝐢 𝐷 ?

Q20:

Given that point 𝐸 bisects 𝐡 𝐢 , point 𝐷 bisects 𝐴 𝐡 , 𝐴 𝐸 and 𝐢 𝐷 intersect at point 𝑀 , and 𝐴 𝐸 = 3 3 c m , find the length of 𝑀 𝐸 .

Q21:

Given that 𝑀 is the point of intersection of the medians, 𝐴 𝐷 = 4 . 3 6 c m , 𝐡 𝑀 = 3 . 4 7 c m , and 𝑀 𝐹 = 1 . 5 9 c m , find the lengths of 𝐴 𝑀 , 𝑀 𝐸 , and 𝐢 𝐹 to the nearest hundredth.

  • A 𝐴 𝑀 = 3 . 2 7 c m , 𝑀 𝐸 = 1 . 1 6 c m , 𝐢 𝐹 = 6 . 3 6 c m
  • B 𝐴 𝑀 = 2 . 1 8 c m , 𝑀 𝐸 = 3 . 4 7 c m , 𝐢 𝐹 = 3 . 1 8 c m
  • C 𝐴 𝑀 = 2 . 9 1 c m , 𝑀 𝐸 = 1 . 7 4 c m , 𝐢 𝐹 = 4 . 7 7 c m

Q22:

In the figure, calculate the length of 𝐴 𝐷 .

Q23:

Given that 𝐸 𝑀 = 1 4 3 c m and 𝐴 𝑀 = 2 𝑀 𝐷 , find the length of 𝐷 𝐹 .

Q24:

Given that 𝐸 𝐷 = 7 . 5 c m , find the lengths of 𝐴 𝐢 and 𝐡 𝐸 .

  • A 𝐴 𝐢 = 2 2 . 5 c m , 𝐡 𝐸 = 1 1 . 2 5 c m
  • B 𝐴 𝐢 = 2 2 . 5 c m , 𝐡 𝐸 = 7 . 5 c m
  • C 𝐴 𝐢 = 1 1 . 2 5 c m , 𝐡 𝐸 = 7 . 5 c m
  • D 𝐴 𝐢 = 1 5 c m , 𝐡 𝐸 = 7 . 5 c m

Q25:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, which line segment is a median in β–³ 𝐴 𝐡 𝐷 ?

  • A 𝐷 𝑀
  • B 𝐡 𝑀
  • C 𝐢 𝑀
  • D 𝐴 𝑀

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