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Statement Reason

x is the midpoint of AB z is the midpoint of AC y is the midpoint of BC AX =BX AZ = CZ BY = CY AB = 2ZY AC = 2XY BC = 2XZ 1/2 AB = ZY 1/2 AC = XY 1/2 BC = XZ 1/2 AB = AX = XB 1/2 AC = AZ = CZ 1/2 BC = BY = CY ZY = AX = XB XY = AX = XB XY = AZ = CZ XZ = CY = BY

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Statement Reason

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  1. x is the midpoint of AB z is the midpoint of AC y is the midpoint of BC AX =BX AZ = CZ BY = CY AB = 2ZY AC = 2XY BC = 2XZ 1/2 AB = ZY 1/2 AC = XY 1/2 BC = XZ 1/2 AB = AX = XB 1/2 AC = AZ = CZ 1/2 BC = BY = CY ZY = AX = XB XY = AX = XB XY = AZ = CZ XZ = CY = BY AXZ = YXZ = XBY = ZYC XYZ similar ABC 4 XYZ = ABC XYZ = ABC/4 Given Definition of a midpoint Medial Triangle Theorem Division Property of Equality Definition of a midpoint Substitution Side Side Side Congruence Side Side Side Similarity Substitution Division Property of Equality Statement Reason

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