Worksheet: Isosceles Triangles

In this worksheet, we will practice using the properties of isosceles triangles to find a missing angle or side length and solve algebraic expressions or equations.

Q1:

Find 𝑚𝐴𝐵𝐶.

Q2:

Find 𝑚𝐵𝐴𝐶.

Q3:

Find 𝑚𝐶𝐵𝐴 and 𝑚𝐷𝐴𝐶.

  • A 𝑚 𝐶 𝐵 𝐴 = 1 0 9 , 𝑚 𝐷 𝐴 𝐶 = 3 8
  • B 𝑚 𝐶 𝐵 𝐴 = 1 0 9 , 𝑚 𝐷 𝐴 𝐶 = 7 1
  • C 𝑚 𝐶 𝐵 𝐴 = 7 1 , 𝑚 𝐷 𝐴 𝐶 = 1 1
  • D 𝑚 𝐶 𝐵 𝐴 = 4 9 , 𝑚 𝐷 𝐴 𝐶 = 7 1

Q4:

Triangle 𝐴𝐵𝐶 is isosceles, with 𝑚𝐶=80. Determine the measures of 𝑥 and 𝑦.

  • A 𝑥 = 8 0 , 𝑦 = 1 0 0
  • B 𝑥 = 1 0 , 𝑦 = 1 7 0
  • C 𝑥 = 5 0 , 𝑦 = 1 0 0
  • D 𝑥 = 5 0 , 𝑦 = 1 3 0

Q5:

Which pair of segments have the same length?

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

Q6:

Find the value of 𝑥.

Q7:

In the figure below, given that 𝐴𝐵=𝐵𝐶, 𝐴𝐷=𝐶𝐷, and 𝑚𝐵𝐴𝐷=108, find 𝑚𝐴𝐷𝐶.

Q8:

Find the values of 𝑥 and 𝑦.

  • A 𝑥 = 8 3 , 𝑦 = 8 7
  • B 𝑥 = 4 1 , 𝑦 = 5
  • C 𝑥 = 9 5 , 𝑦 = 1 1
  • D 𝑥 = 4 1 , 𝑦 = 1 1
  • E 𝑥 = 9 5 , 𝑦 = 5

Q9:

In the figure, given that 𝐴𝐷=𝐴𝐶=𝐶𝐵 and 𝑚𝐷=52, find 𝑚𝐷𝐴𝐵.

  • A 1 2 8
  • B 1 3 0
  • C 1 0 2
  • D 1 0 4
  • E 5 2

Q10:

In the displayed model of a house, what angle does the roof make with the horizontal, given that 𝐴𝐸𝐵 is isosceles?

Q11:

Find the value of 𝑥 in the figure below.

Q12:

Given that 𝑚𝐵=(3𝑥+52.5) and 𝑚𝐶=(2𝑥+53.5), find the measures of the angles of 𝐴𝐵𝐶.

  • A 𝑚 𝐴 = 5 5 . 5 , 𝑚 𝐵 = 6 9 , 𝑚 𝐶 = 5 5 . 5
  • B 𝑚 𝐴 = 1 2 4 . 5 , 𝑚 𝐵 = 5 5 . 5 , 𝑚 𝐶 = 5 5 . 5
  • C 𝑚 𝐴 = 6 9 , 𝑚 𝐵 = 5 5 . 5 , 𝑚 𝐶 = 5 5 . 5

Q13:

In the following figure, find the value of 𝑥.

Q14:

Find the values of 𝑥 and 𝑦.

  • A 𝑥 = 1 5 , 𝑦 = 8
  • B 𝑥 = 1 5 , 𝑦 = 2
  • C 𝑥 = 3 0 , 𝑦 = 2
  • D 𝑥 = 7 . 5 , 𝑦 = 6
  • E 𝑥 = 3 0 , 𝑦 = 8

Q15:

Given that 𝐴𝐷=𝐷𝐶=𝐶𝐵=𝐵𝐷, find the value of 𝑥.

  • A 8 5
  • B 2 4
  • C 6
  • D 1 8

Q16:

Find the values of 𝑥 and 𝑦.

  • A 𝑥 = 7 8 , 𝑦 = 9
  • B 𝑥 = 3 0 , 𝑦 = 9
  • C 𝑥 = 3 0 , 𝑦 = 3
  • D 𝑥 = 1 2 , 𝑦 = 3
  • E 𝑥 = 1 2 , 𝑦 = 9

Q17:

Find all possible values of 𝑥.

  • A 𝑥 = 1 0 or 𝑥=4
  • B 𝑥 = 3 4 or 𝑥=46
  • C 𝑥 = 1 0 or 𝑥=4
  • D 𝑥 = 1 0 or 𝑥=4
  • E 𝑥 = 1 0 or 𝑥=4

Q18:

In the figure, determine all possible values of 𝑦.

  • A 𝑦 = 3 or 𝑦=1
  • B 𝑦 = 2 or 𝑦=3
  • C 𝑦 = 3 or 𝑦=1
  • D 𝑦 = 3 or 𝑦=1
  • E 𝑦 = 3 or 𝑦=1

Q19:

In the figure below, given that 𝐴𝐷=𝐷𝐶=𝐴𝐶, 𝐴𝐵=𝐵𝐶, and 𝑚𝐴𝐵𝐶=54, determine 𝑚𝐵𝐴𝐷.

Q20:

Find 𝑚𝐵𝐸𝐴 and 𝑚𝐸𝐴𝐶.

  • A 𝑚 𝐵 𝐸 𝐴 = 7 2 , 𝑚 𝐸 𝐴 𝐶 = 3 6
  • B 𝑚 𝐵 𝐸 𝐴 = 3 6 , 𝑚 𝐸 𝐴 𝐶 = 1 3 2
  • C 𝑚 𝐵 𝐸 𝐴 = 1 3 2 , 𝑚 𝐸 𝐴 𝐶 = 7 2
  • D 𝑚 𝐵 𝐸 𝐴 = 7 2 , 𝑚 𝐸 𝐴 𝐶 = 1 3 2

Q21:

If 𝐴𝐵𝐶 has one line of symmetry, and 𝑚𝐴𝐵𝐶=128, find 𝑚𝐴.

Q22:

In an isosceles triangle 𝐴𝐵𝐶, 𝐴𝐵=𝐴𝐶, 𝐵𝐶=60cm, 𝐴𝐷 is perpendicular to 𝐵𝐶 and intersecting the segment at 𝐷, and 𝑚𝐵𝐴𝐷=26. Find the length of 𝐵𝐷 and 𝑚𝐵.

  • A 60 cm, 6 4
  • B 30 cm, 2 6
  • C 30 cm, 6 4
  • D 60 cm, 2 6

Q23:

Which of the following is true?

  • A 𝐴 𝐵 = 𝐴 𝐶
  • B 𝐵 𝐶 = 𝐵 𝐴
  • C 𝐶 𝐴 = 𝐶 𝐵

Q24:

Is 𝑀𝐵𝐶 an isosceles triangle?

  • ANo
  • BYes

Q25:

Find 𝑚𝐵𝐷𝐸.

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