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Worksheet: Isosceles Triangles

In this worksheet, we will practice identifying isosceles triangles to find a missing angle or side length.

Q1:

Find π‘š ∠ 𝐴 𝐡 𝐢 .

Q2:

Find π‘š ∠ 𝐡 𝐴 𝐢 .

Q3:

Find π‘š ∠ 𝐢 𝐡 𝐴 and π‘š ∠ 𝐷 𝐴 𝐢 .

  • A π‘š ∠ 𝐢 𝐡 𝐴 = 1 0 9 ∘ , π‘š ∠ 𝐷 𝐴 𝐢 = 3 8 ∘
  • B π‘š ∠ 𝐢 𝐡 𝐴 = 4 9 ∘ , π‘š ∠ 𝐷 𝐴 𝐢 = 7 1 ∘
  • C π‘š ∠ 𝐢 𝐡 𝐴 = 1 0 9 ∘ , π‘š ∠ 𝐷 𝐴 𝐢 = 7 1 ∘
  • D π‘š ∠ 𝐢 𝐡 𝐴 = 7 1 ∘ , π‘š ∠ 𝐷 𝐴 𝐢 = 1 1 ∘

Q4:

Triangle 𝐴 𝐡 𝐢 is isosceles, with π‘š ∠ 𝐢 = 8 0 ∘ . Determine the measures of π‘₯ and 𝑦 .

  • A π‘₯ = 1 0 ∘ , 𝑦 = 1 7 0 ∘
  • B π‘₯ = 8 0 ∘ , 𝑦 = 1 0 0 ∘
  • C π‘₯ = 5 0 ∘ , 𝑦 = 1 0 0 ∘
  • D π‘₯ = 5 0 ∘ , 𝑦 = 1 3 0 ∘

Q5:

Which pair of segments have the same length?

  • A ,
  • B ,
  • C ,

Q6:

Find the value of π‘₯ .

Q7:

In the figure below, given that 𝐴 𝐡 = 𝐡 𝐢 , 𝐴 𝐷 = 𝐢 𝐷 , and π‘š ∠ 𝐡 𝐴 𝐷 = 1 0 8 ∘ , find π‘š ∠ 𝐴 𝐷 𝐢 .

Q8:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 4 1 , 𝑦 = 1 1
  • B π‘₯ = 9 5 , 𝑦 = 1 1
  • C π‘₯ = 9 5 , 𝑦 = 5
  • D π‘₯ = 4 1 , 𝑦 = 5
  • E π‘₯ = 8 3 , 𝑦 = 8 7

Q9:

In the figure, given that 𝐴 𝐷 = 𝐴 𝐢 = 𝐢 𝐡 and π‘š ∠ 𝐷 = 5 2 ∘ , find π‘š ∠ 𝐷 𝐴 𝐡 .

Q10:

In the displayed model of a house, what angle does the roof make with the horizontal, given that β–³ 𝐴 𝐸 𝐡 is isosceles?

Q11:

Find the value of π‘₯ in the figure below.

Q12:

Given that π‘š ∠ 𝐡 = ( 3 π‘₯ + 5 2 . 5 ) ∘ and π‘š ∠ 𝐢 = ( 2 π‘₯ + 5 3 . 5 ) ∘ , find the measures of the angles of β–³ 𝐴 𝐡 𝐢 .

  • A π‘š ∠ 𝐴 = 5 5 . 5 ∘ , π‘š ∠ 𝐡 = 6 9 ∘ , π‘š ∠ 𝐢 = 5 5 . 5 ∘
  • B π‘š ∠ 𝐴 = 1 2 4 . 5 ∘ , π‘š ∠ 𝐡 = 5 5 . 5 ∘ , π‘š ∠ 𝐢 = 5 5 . 5 ∘
  • C π‘š ∠ 𝐴 = 6 9 ∘ , π‘š ∠ 𝐡 = 5 5 . 5 ∘ , π‘š ∠ 𝐢 = 5 5 . 5 ∘

Q13:

In the following figure, find the value of π‘₯ .

Q14:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 3 0 , 𝑦 = 2
  • B π‘₯ = 7 . 5 , 𝑦 = 6
  • C π‘₯ = 1 5 , 𝑦 = 8
  • D π‘₯ = 1 5 , 𝑦 = 2
  • E π‘₯ = 3 0 , 𝑦 = 8

Q15:

Given that 𝐴 𝐷 = 𝐷 𝐢 = 𝐢 𝐡 = 𝐡 𝐷 , find the value of π‘₯ .

  • A βˆ’ 6
  • B 2 4
  • C 8 5
  • D 1 8

Q16:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 2 , 𝑦 = 3
  • B π‘₯ = 3 0 , 𝑦 = 3
  • C π‘₯ = 3 0 , 𝑦 = 9
  • D π‘₯ = 1 2 , 𝑦 = 9
  • E π‘₯ = 7 8 , 𝑦 = 9

Q17:

Find all possible values of π‘₯ .

  • A π‘₯ = 1 0 or π‘₯ = 4
  • B π‘₯ = 3 4 or π‘₯ = 4 6
  • C π‘₯ = βˆ’ 1 0 or π‘₯ = βˆ’ 4
  • D π‘₯ = 1 0 or π‘₯ = βˆ’ 4
  • E π‘₯ = βˆ’ 1 0 or π‘₯ = 4

Q18:

In the figure, determine all possible values of 𝑦 .

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

Q19:

In the figure below, given that 𝐴 𝐷 = 𝐷 𝐢 = 𝐴 𝐢 , 𝐴 𝐡 = 𝐡 𝐢 , and π‘š ∠ 𝐴 𝐡 𝐢 = 5 4 ∘ , determine π‘š ∠ 𝐡 𝐴 𝐷 .

Q20:

Find π‘š ∠ 𝐡 𝐸 𝐴 and π‘š ∠ 𝐸 𝐴 𝐢 .

  • A π‘š ∠ 𝐡 𝐸 𝐴 = 3 6 ∘ , π‘š ∠ 𝐸 𝐴 𝐢 = 1 3 2 ∘
  • B π‘š ∠ 𝐡 𝐸 𝐴 = 1 3 2 ∘ , π‘š ∠ 𝐸 𝐴 𝐢 = 7 2 ∘
  • C π‘š ∠ 𝐡 𝐸 𝐴 = 7 2 ∘ , π‘š ∠ 𝐸 𝐴 𝐢 = 3 6 ∘
  • D π‘š ∠ 𝐡 𝐸 𝐴 = 7 2 ∘ , π‘š ∠ 𝐸 𝐴 𝐢 = 1 3 2 ∘

Q21:

If β–³ 𝐴 𝐡 𝐢 has one line of symmetry, and π‘š ∠ 𝐴 𝐡 𝐢 = 1 2 8 ∘ , find π‘š ∠ 𝐴 .

Q22:

In an isosceles triangle 𝐴 𝐡 𝐢 , 𝐴 𝐡 = 𝐴 𝐢 , 𝐡 𝐢 = 6 0 c m , 𝐴 𝐷 is perpendicular to 𝐡 𝐢 and intersecting the segment at 𝐷 , and π‘š ∠ 𝐡 𝐴 𝐷 = 2 6 ∘ . Find the length of 𝐡 𝐷 and π‘š ∠ 𝐡 .

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

Q23:

Which of the following is true?

  • A 𝐡 𝐢 = 𝐡 𝐴
  • B 𝐴 𝐡 = 𝐴 𝐢
  • C 𝐢 𝐴 = 𝐢 𝐡

Q24:

Is 𝑀 𝐡 𝐢 an isosceles triangle?

  • AYes
  • BNo

Q25:

Find π‘š ∠ 𝐡 𝐷 𝐸 .

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