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 2 years ago
Complete the proof below. Be sure to number your responses 1, 2, 3, and 4 (one point each).
Theorem 58
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram.
R
Given: and
Prove: Quadrilateral H K I J is a parallelogram.
Paragraph Proof: We are given that JI II HK andJI=HK . Diagonals IH and HK are drawn intersecting at point L.1=4 and2=3 because __(1)__ are congruent. This allows us to prove that IJL =HKI by __(2)__. This allows us to state that IL= HL andJL= KL because __(3)__. In other words, diagonals IH and JK __(4)__ each other by the definition of bisector According to Theorem 57, quadrilateral HKIJ is a parallelogram because the diagonalsIH and JK bisect each other.
 2 years ago
Complete the proof below. Be sure to number your responses 1, 2, 3, and 4 (one point each). Theorem 58 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. R Given: and Prove: Quadrilateral H K I J is a parallelogram. Paragraph Proof: We are given that JI II HK andJI=HK . Diagonals IH and HK are drawn intersecting at point L.1=4 and2=3 because __(1)__ are congruent. This allows us to prove that IJL =HKI by __(2)__. This allows us to state that IL= HL andJL= KL because __(3)__. In other words, diagonals IH and JK __(4)__ each other by the definition of bisector According to Theorem 57, quadrilateral HKIJ is a parallelogram because the diagonalsIH and JK bisect each other.

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