Lesson Worksheet: Isosceles Triangle Theorems Mathematics • 11th Grade

In this worksheet, we will practice using the isosceles triangle theorems to find missing lengths and angles in isosceles triangles.


Consider the following triangle.

Identify the legs of the triangle.

  • A𝐴𝐡 and 𝐴𝐢
  • B𝐴𝐡 and 𝐡𝐢
  • C𝐡𝐢 and 𝐴𝐢


In the following triangle, 𝐴𝐡=3cm, 𝐡𝐢=3cm, and 𝐴𝐢=4cm.

Identify the base angles of this triangle.

  • A∠𝐴 and ∠𝐢
  • B∠𝐴 and ∠𝐡
  • C∠𝐢 and ∠𝐡


Find π‘šβˆ π΅π΄πΆ.


Find π‘šβˆ πΆπ΅π΄ and π‘šβˆ π·π΄πΆ.

  • Aπ‘šβˆ πΆπ΅π΄=109∘, π‘šβˆ π·π΄πΆ=38∘
  • Bπ‘šβˆ πΆπ΅π΄=109∘, π‘šβˆ π·π΄πΆ=71∘
  • Cπ‘šβˆ πΆπ΅π΄=71∘, π‘šβˆ π·π΄πΆ=11∘
  • Dπ‘šβˆ πΆπ΅π΄=49∘, π‘šβˆ π·π΄πΆ=71∘


Find the measures of the angles of △𝐴𝐡𝐢.

  • Aπ‘šβˆ π΄π΅πΆ=39.5∘, π‘šβˆ π΅π΄πΆ=39.5∘, π‘šβˆ π΄πΆπ΅=101∘
  • Bπ‘šβˆ π΄π΅πΆ=19.75∘, π‘šβˆ π΅π΄πΆ=140.5∘, π‘šβˆ π΄πΆπ΅=19.75∘
  • Cπ‘šβˆ π΄π΅πΆ=50.5∘, π‘šβˆ π΅π΄πΆ=50.5∘, π‘šβˆ π΄πΆπ΅=79∘
  • Dπ‘šβˆ π΄π΅πΆ=70.25∘, π‘šβˆ π΅π΄πΆ=70.25∘, π‘šβˆ π΄πΆπ΅=39.5∘


Which pair of segments have the same length?

  • A𝐴𝐡, 𝐡𝐢
  • B𝐴𝐢, 𝐡𝐢
  • C𝐴𝐡, 𝐴𝐢


Given that π‘šβˆ πΉπΆπ΄=134∘ in the figure below, two sides are equal, which are these?

  • A𝐴𝐡, 𝐡𝐢
  • B𝐴𝐢, 𝐡𝐢
  • C𝐴𝐡, 𝐴𝐢
  • D𝐷𝐸, 𝐢𝐹


In the figure, find 𝐴𝐷 given that 𝐡𝐸=6cm and 𝐴𝐸=6cm.


Is 𝑀𝐡𝐢 an isosceles triangle?

  • ANo
  • BYes


Is the triangle 𝐴𝐡𝐢 isosceles?

  • AYes
  • BNo

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