Prove that ABCD is a parallelogram \overline{AB}\parallel \overline{CD}, \overline{AB}\cong \overline{DC}

Burhan Hopper

Burhan Hopper

Answered question

2021-07-26

To prove: ABCD is a parallelogram.
Given information:
ABparallCD,
AB=DC.

Answer & Explanation

cheekabooy

cheekabooy

Skilled2021-07-27Added 83 answers

Proof:

It is given that,
AB=CD,
AD=BC.
If lines are parallel, alternate interior angles are congruent.
CDB=ABD
DCA=BAC
Two triangles are congruent by ASA congruence rule.
ABX=CDX
Corresponding parts of congruent triangles are congruent.
AX=XC
BX=XD
Vertical angles are congruent.
AXD=BXC
Two triangles are congruent by SAS congruence rule.
AXD=CXB
Corresponding parts of congruent triangles are congruent.
BC=AD
If both pairs of opposite sides are congruent, then a quadrilateral is a parallelogram.
ABCD is a parallelogram.

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