Consider the diagram and proof by contradiction. Given: △ABC with ∠B ≅ ∠C Prove: AB ≅ AC It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC. What is the missing reason in the proof? converse of the triangle parts relationship theorem substitution definition of congruency converse of the isosceles triangle theorem

QUESTION POSTED AT 01/06/2020 - 04:31 PM

Answered by admin AT 01/06/2020 - 04:31 PM

The Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side.

The converse to the
Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one angle of a triangle has a greater degree measure than another angle, then the side opposite the greater angle will be longer than the side opposite the smaller angle.

Thus, from the proof if AB > AC, then m∠C > m∠B by the converse of the triangle parts relationship theorem.

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