Question

in a parallelogram ABCD , E is the midpoint of the diagonal AC. PQ is the line passing through E. P,Q are the points of intersection with side AB and DC respectively. prove that seg PE = seg EQ​

Answer 1

$\huge\underbrace{\orange{\tt{Solution:}}}$

Given:

• ABCD is a Parallelogram

• AC is the diagonal, E is the mid point of AC& AE = EC

• PQ is the line (transversal) drawn through AB & DC

Required To Prove:

◕➜ PE = EQ

Proof:

In ∆AEP & ∆CEQ

AE = CE (Given)

∠AEP = ∠CEQ (Vertically Opposite Angles)

∠PAE = ∠QCE (Alternative Interior Angles)

[As AB || CD & AC as Transversal]

Thus, ∆AEP ≅ ∆CEQ [By ASA Axiom]

By CPCT, $\Large\red{\sf{PE = EQ}}$

Hence, Proved

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