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Claudiu Papasteri · Answer 1 · 2023-03-03T08:15:29+0000

Consider triangle ABE and triangle CDE,

$ABCD\text{ is a parallelogram (Given)}$
$AB\parallel CD\text{ (Defination of a parallelogram (1))}$
$\angle1\cong\angle2,\angle3\cong\angle4\text{ (Alternate interior angle thorem)}$
$AB\cong CD\text{ (Defination of a parallelogram (2))}$
$\Delta ABE\cong\Delta CDE\text{ (ASA)}$
$AE\cong CE,BE\cong DE\text{ (CPCTC)}$
$AC\text{ and BD bisect each other at E (Defination of segment bisector)}$

Answer:

Given

Defination of a parallelogram (1)

Alternate interior angles theorem

Defination of a parallelogram (2)

ASA

CPCTC

Defination of segment bisector

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