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Worksheet: Corollaries of Isosceles Triangle Theorems

Q1:

What is π‘š ∠ 𝑋 𝐢 𝐡 ?

  • A 1 6 8 ∘
  • B 8 4 ∘
  • C 6 4 ∘
  • D 5 2 ∘

Q2:

Find π‘₯ .

Q3:

In the following figure, find the length of 𝐾 𝐿 .

Q4:

In the figure, what is the length of 𝐸 𝐺 ?

Q5:

Find the length of 𝐴 𝐢 and π‘š ∠ 𝐷 𝐡 𝐢 .

  • A 116 cm, 6 0 ∘
  • B 116 cm, 3 0 ∘
  • C 58 cm, 4 5 ∘
  • D 116 cm, 4 5 ∘
  • E 58 cm, 3 0 ∘

Q6:

Find π‘š ∠ 𝐷 𝐴 𝐡 .

Q7:

In β–³ 𝐴 𝐡 𝐢 , if 𝐴 𝐡 = 𝐴 𝐢 and π‘š ∠ 𝐴 = 5 2 ∘ , find π‘š ∠ 𝐡 .

Q8:

In the figure below, what is the area of β–³ 𝑋 π‘Œ 𝑍 ?

Q9:

In the following figure, find the length of π‘Š π‘Œ .

Q10:

The given figure shows an isosceles triangle, where 𝑀 is the midpoint of 𝐴 𝐡 .

Can we prove that triangle 𝐴 𝐢 𝑀 and triangle 𝐡 𝐢 𝑀 are congruent? If yes, state which congruence criteria could be used.

  • AYes, SAS
  • BNo
  • CYes, ASA
  • DYes, SSS

Hence, what can we conclude about the angles 𝐢 𝐴 𝐡 and 𝐴 𝐡 𝐢 ?

  • AWe cannot conclude anything, because we need more information.
  • BThe angle 𝐴 𝐡 𝐢 is bigger than the angle 𝐢 𝐴 𝐡 , because the two triangles are congruent.
  • CThe angle 𝐢 𝐴 𝐡 is bigger than the angle 𝐴 𝐡 𝐢 , because the two triangles are congruent.
  • DThe angles have the same measure, because the triangles are congruent.

Q11:

Given that 𝐢 𝐴 = 𝐢 𝐷 = 𝐴 𝐡 , π‘š ∠ 𝐷 𝐢 𝐴 = 4 8 ∘ , and π‘š ∠ 𝐴 𝐡 𝐢 = ( 3 π‘₯ + 2 1 ) ∘ , find the value of π‘₯ .