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LC Math 2 Adv – Isosceles Triangle Theorem (LT 2)
Part 1 – Construction
What must be constructed to form an isosceles triangle?
Use your compass and straightedge to construct an isosceles triangle in the space below.
Along with your partner, use inductive reasoning to make a postulate about isosceles triangles. Explain below.
Part 2 – Transformations
Britney proposes an argument for why 𝑚∠𝐵 must equal 𝑚∠𝐶.
She says:
“If I draw the bisector of ∠A then this is a line of symmetry for △ABC and
so m(∠B)=m(∠C).”
a) What additional information is provided when you draw the bisector of ∠A?
b) How can you add to Britney’s argument to make it more complete? Write a full explanation of her reasoning
process below.
c) If the two triangles formed in Britney’s argument can be mapped onto one another using a sequence of
isometries, what conclusion can be drawn?
Part 3 – Proof
Isosceles Triangle Theorem: If two sides of a triangle are congruent, then
the angles opposite those sides are congruent.
Use the understanding from Britney’s reasoning to complete a proof
of the Isosceles Triangle Theorem.
Given: ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐴𝐶
Prove: ∠𝐵 ≅ ∠𝐶
Statement
Reason
Part 4 – Proof of the Converse
Converse of the Isosceles Triangle Theorem: If two angles of a triangle are
congruent, then the sides opposite those angles are congruent.
Use the understanding from Britney’s reasoning to complete a proof
of the Converse of the Isosceles Triangle Theorem.
Given: ∠𝑃 ≅ ∠𝑄
̅̅̅̅
̅̅̅̅ ≅ 𝑅𝑄
Prove: 𝑅𝑃
Statement
Reason