Provide the missing parts in the following proof of the SsA Congruence Theorem. Given: ∆ABC and ∆XYZ with AB = XY, BC = YZ, ∠A ≡ ∠X, and BC ≥ BA. Prove: ∆ABC = ∆XYZ.
CONCLUSIONS | JUSTIFICATIONS |
(1) Suppose the triangles are not congruent. | Given |
(2) Then L C and LZ are supplementary angles. | (a)____? |
(3) One of the angles, say Z.Z, is either a right angle, or an obtuse angle. | Definition of supplementary angles |
(4) m∠Z > m∠X | A triangle has at most one right angle or obtuse angle |
(b) ______? | Scalene Inequality |
(5) AB > BC. →← | (c) ______? |
(6) ∴ ∆ABC = ∆XYZ. | The only remaining possibility |
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