Worksheet: Medians of Triangles

In this worksheet, we will practice identifying the medians of a triangle and using their properties of proportionality to find a missing length.

Q1:

In β–³π‘‹π‘Œπ‘, where 𝐴 is the midpoint of π‘‹π‘Œ, what name is given to 𝐴𝑍?

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

Q2:

In a triangle 𝐴𝐡𝐢, 𝑀 is the point of concurrency of its medians. If 𝐴𝐷 is a median, then 𝐴𝑀=𝑀𝐷.

  • A 2 3
  • B 1 2
  • C2
  • D 1 3

Q3:

What is length 𝑀𝐡 rounded to the nearest hundredth?

Q4:

Find the length 𝐴𝑀, given that 𝐴𝐸=54.

Q5:

Determine the lengths of 𝐡𝐷 and 𝐴𝐡.

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

Q6:

In △𝐽𝐾𝐿, 𝑅𝑃=2.1cm. Find the length of 𝑃𝐿.

Q7:

In △𝐾𝑀𝐻, 𝐾𝑄=2 and 𝑄𝑃=(5π‘₯βˆ’7). Find π‘₯.

Q8:

In the given figure, segments 𝐴𝐷 and 𝐢𝐸 are the medians of △𝐴𝐢𝐡, where π΄π·βŸ‚πΆπΈ, 𝐴𝐡=17.7cm, and 𝐢𝐸=9cm. Determine 𝐢𝐴 to the nearest tenth.

Q9:

In △𝐽𝐾𝐿, 𝐽𝑃=6cm. Find the length of 𝑃𝑆.

Q10:

Given that the area of △𝐴𝐸𝐢=63cm, find the area of △𝐴𝐡𝐢.

Q11:

Find the length of 𝐡𝐷 and the perimeter of △𝐴𝐡𝐷.

  • A 𝐡 𝐷 = 2 . 2 5 c m , perimeter of △𝐴𝐡𝐷=15cm
  • B 𝐡 𝐷 = 4 . 5 c m , perimeter of △𝐴𝐡𝐷=15cm
  • C 𝐡 𝐷 = 9 c m , perimeter of △𝐴𝐡𝐷=18cm
  • D 𝐡 𝐷 = 4 . 5 c m , perimeter of △𝐴𝐡𝐷=13.5cm

Q12:

Equilateral triangle 𝐴𝐡𝐢 has side 50.6. Given that 𝑀 is the intersection of its medians, determine 𝑀𝐡⋅𝐢𝑀.

Q13:

Given that 𝑃𝐾 is a median of △𝐽𝐿𝑃, 𝐽𝐾=3π‘¦βˆ’8, and 𝐿𝐾=2π‘¦βˆ’4, find the length of 𝐿𝐾.

Q14:

Use the data in the figure to determine the length of 𝐷𝐹 and then the perimeter of △𝐷𝐸𝐹.

  • A length of 𝐷𝐹=18cm, perimeter of △𝐷𝐸𝐹=88cm
  • B length of 𝐷𝐹=30cm, perimeter of △𝐷𝐸𝐹=90cm
  • C length of 𝐷𝐹=22cm, perimeter of △𝐷𝐸𝐹=131cm
  • D length of 𝐷𝐹=24.5cm, perimeter of △𝐷𝐸𝐹=65.5cm

Q15:

In triangle 𝐴𝐡𝐢, 𝐴𝐡=𝐴𝐢=10cm, 𝐡𝐢=12cm and 𝐷 is the midpoint of 𝐡𝐢. Find the length of 𝐴𝐷.

Q16:

In triangle 𝐴𝐡𝐢, 𝐴𝐡=𝐴𝐢=10cm, 𝐡𝐢=16cm and 𝐷 is the midpoint of 𝐡𝐢. Find the length of 𝐴𝐷.

Q17:

Given that 𝐴𝐷=9cm and 𝐸𝐡=𝐴𝐡, find the perimeter of △𝑀𝐷𝐸.

Q18:

Given that 𝐴𝐡=𝐴𝐢=22cm, 𝐢𝐡=20cm, and 𝐸𝐡=𝐸𝐢, find the length of 𝐴𝐷.

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

Q19:

What is the length of 𝐢𝐷?

Q20:

Given that point 𝐸 bisects 𝐡𝐢, point 𝐷 bisects 𝐴𝐡, 𝐴𝐸 and 𝐢𝐷 intersect at point 𝑀, and 𝐴𝐸=33cm, find the length of 𝑀𝐸.

Q21:

Given that 𝑀 is the point of intersection of the medians, 𝐴𝐷=4.36cm, 𝐡𝑀=3.47cm, and 𝑀𝐹=1.59cm, find the lengths of 𝐴𝑀, 𝑀𝐸, and 𝐢𝐹 to the nearest hundredth.

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

Q22:

Given that 𝐸𝑀=143cm and 𝐴𝑀=2𝑀𝐷, find the length of 𝐷𝐹.

Q23:

Given that 𝐸𝐷=7.5cm, find the lengths of 𝐴𝐢 and 𝐡𝐸.

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

Q24:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram, which line segment is a median in △𝐴𝐡𝐷?

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

Q25:

Given that 𝑀𝐡=84cm and 𝐢𝐷=96cm, find the perimeter of △𝐷𝑀𝐸.

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