Question

prove that a quadrilateral with both pairs of opposite sides congruent must be a parallelogram given segment PL is congruent to segment GM AND SEGMENT LG is congruent to segment MP prove PLGM is a parallelogram

Answer 1

prove that a quadrilateral with both pairs of opposite sides congruent must be a parallelogram given segment PL is congruent to segment GM AND SEGMENT LG is congruent to segment MP proves PLGM is a parallelogram

see the attached figure

we have that

1) PL=GM -------> given

2) LG=MP-------> given

3) ML=LM -----> Common side, reflexive property of equality

4) ΔMPL ≅ΔLGM -------> SSS ;postulate

5) ∠MPL≅∠LGM ------> by Corresponding angles in congruent triangles

that prove that the quadrilateral has opposite sides parallel and congruent, and opposite angles congruent, that is the definition of the parallelogram