Consider the diagram and proof by contradiction.
Given: △ABC with AB ≅ AC
Triangle A B...
Mathematics, 17.12.2020 20:50, pacetys
Consider the diagram and proof by contradiction.
Given: △ABC with AB ≅ AC
Triangle A B C is shown. The lengths of sides A B and A C are congruent.
Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that .
AB ≠ AC
∠B ≅ ∠C
ABC is not a triangle
∠A ≅ ∠B ≅ ∠C
Answers: 1
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