Given: ΔABC is isosceles; AB ≅ AC
Prove: ∠B ≅ ∠C
Triangle A B C is shown. Sides B A and...
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Mathematics, 20.02.2021 01:00 samanthaurso1
Given: ΔABC is isosceles; AB ≅ AC
Prove: ∠B ≅ ∠C
Triangle A B C is shown. Sides B A and A C are congruent.
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that
.
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the
.
However, this contradicts the given information that
. Therefore,
, which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.
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