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.

  • A𝑚𝐶𝐵𝐴=109, 𝑚𝐷𝐴𝐶=38
  • B𝑚𝐶𝐵𝐴=109, 𝑚𝐷𝐴𝐶=71
  • C𝑚𝐶𝐵𝐴=71, 𝑚𝐷𝐴𝐶=11
  • D𝑚𝐶𝐵𝐴=49, 𝑚𝐷𝐴𝐶=71

Q4:

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

  • A𝑥=80, 𝑦=100
  • B𝑥=10, 𝑦=170
  • C𝑥=50, 𝑦=100
  • D𝑥=50, 𝑦=130

Q5:

Which pair of segments have the same length?

  • A𝐴𝐵, 𝐵𝐶
  • B𝐴𝐶, 𝐵𝐶
  • C𝐴𝐵, 𝐴𝐶

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.

  • A𝑥=83, 𝑦=87
  • B𝑥=41, 𝑦=5
  • C𝑥=95, 𝑦=11
  • D𝑥=41, 𝑦=11
  • E𝑥=95, 𝑦=5

Q9:

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

  • A128
  • B130
  • C102
  • D104
  • E52

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.

  • A𝑚𝐴=55.5, 𝑚𝐵=69, 𝑚𝐶=55.5
  • B𝑚𝐴=124.5, 𝑚𝐵=55.5, 𝑚𝐶=55.5
  • C𝑚𝐴=69, 𝑚𝐵=55.5, 𝑚𝐶=55.5

Q13:

In the following figure, find the value of 𝑥.

Q14:

Find the values of 𝑥 and 𝑦.

  • A𝑥=15, 𝑦=8
  • B𝑥=15, 𝑦=2
  • C𝑥=30, 𝑦=2
  • D𝑥=7.5, 𝑦=6
  • E𝑥=30, 𝑦=8

Q15:

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

  • A85
  • B24
  • C6
  • D18

Q16:

Find the values of 𝑥 and 𝑦.

  • A𝑥=78, 𝑦=9
  • B𝑥=30, 𝑦=9
  • C𝑥=30, 𝑦=3
  • D𝑥=12, 𝑦=3
  • E𝑥=12, 𝑦=9

Q17:

Find all possible values of 𝑥.

  • A𝑥=10 or 𝑥=4
  • B𝑥=34 or 𝑥=46
  • C𝑥=10 or 𝑥=4
  • D𝑥=10 or 𝑥=4
  • E𝑥=10 or 𝑥=4

Q18:

In the figure, determine all possible values of 𝑦.

  • A𝑦=3 or 𝑦=1
  • B𝑦=2 or 𝑦=3
  • C𝑦=3 or 𝑦=1
  • D𝑦=3 or 𝑦=1
  • E𝑦=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.

  • A𝑚𝐵𝐸𝐴=72, 𝑚𝐸𝐴𝐶=36
  • B𝑚𝐵𝐸𝐴=36, 𝑚𝐸𝐴𝐶=132
  • C𝑚𝐵𝐸𝐴=132, 𝑚𝐸𝐴𝐶=72
  • D𝑚𝐵𝐸𝐴=72, 𝑚𝐸𝐴𝐶=132

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.

  • A60 cm, 64
  • B30 cm, 26
  • C30 cm, 64
  • D60 cm, 26

Q23:

Which of the following is true?

  • A𝐴𝐵=𝐴𝐶
  • B𝐵𝐶=𝐵𝐴
  • C𝐶𝐴=𝐶𝐵

Q24:

Is 𝑀𝐵𝐶 an isosceles triangle?

  • ANo
  • BYes

Q25:

Find 𝑚𝐵𝐷𝐸.

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