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3.3 I can apply postulates and algebraic proofs to prove statements. NAME___________________________ Geometry Proofs Match the situation with the likely reasoning/postulate. 1. M is the midpoint of AB, so AM = MB. 2. HG is the angle bisector of ∠ XHZ, so ∠ XHG = ∠ GHZ. 3. Two segments need to be totaled together. 4. Two angles need to be totaled together. 5. One segment has the same measure as another segment. 6. One angle has the same measure as another angle. A. Angle Addition Postulate B. Definition of Congruent Segments C. Definition of Midpoint D. Segment Addition Postulate E. Definition of Angle Bisector F. Definition of Congruent Angles MARK THE DIAGRAM WITH THE GIVEN INFORMATION. Then, fill in the blanks to complete the proofs. 7. Given LS = LS AL + LS = SK + LS AL + LS = AS Segment Addition Postulate Segment Addition Postulate AS = LK Substitution Property 8. ̅̅̅̅ ⊥ 𝐵𝐷 ̅̅̅̅ 𝐴𝐵 ∠ is a right angle 𝑚∠𝐴𝐵𝐷 = ______ Def. of Perpendicular Lines Def. of a Right Angle 𝑚∠𝐴𝐵𝐷 = 𝑚∠1 + 𝑚∠2 𝑚∠1 + 𝑚∠2 = 90° Given 𝑚∠1 + 𝑚∠3 = 90° 9. 10. 11. Def. of Angle Bisector ∠𝐴𝐵𝐷 + ∠𝐷𝐵𝐶 = ___________ ∠𝐴𝐵𝐷 + ∠________ = ∠_________ Substitution Property 2 ⋅ ∠________ = ∠𝐴𝐵𝐶 Combining Like Terms Division Property of Eq.