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Worksheet: Identifying Isosceles Triangles to Find a Missing Angle or Side Length

Q1:

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

Q2:

In the figure below, given that , , and , determine .

  • A
  • B
  • C
  • D
  • E

Q3:

In the figure below, given that , , and , find .

  • A
  • B
  • C
  • D

Q4:

Find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q5:

Find .

  • A
  • B
  • C
  • D

Q6:

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

Q7:

If has one line of symmetry, and , find .

  • A
  • B
  • C

Q8:

In an isosceles triangle , , , is perpendicular to and intersecting the segment at , and . Find the length of and .

  • A 60 cm,
  • B 30 cm,
  • C 60 cm,
  • D 30 cm,

Q9:

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

Q10:

Which of the following is true?

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

Q11:

Is 𝑀 𝐡 𝐢 an isosceles triangle?

  • AYes
  • BNo

Q12:

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

Q13:

Find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q14:

Find .

  • A
  • B
  • C
  • D

Q15:

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

Q16:

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?

Q17:

Find the value of π‘₯ .

Q18:

Which pair of segments have the same length?

  • A ,
  • B ,
  • C ,

Q19:

Triangle is isosceles, with . Determine the sizes of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q20:

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

Q21:

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

  • A 1 3
  • B 1 7
  • C 1 8
  • D 7

Q22:

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

Q23:

In the figure, given that and , find .

  • A
  • B
  • C
  • D
  • E

Q24:

Given that and , find the sizes of the angles of .

  • A , ,
  • B , ,
  • C , ,

Q25:

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