In the given figure, LAXM is a parallelogram. Point I is the midpoint of diagonal LX. PQ is a line passing through point L. The points P and Q are the points of intersection of side LA and side MX respectively, Prove that seg PI is congruent seg IQ
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Step-by-step explanation:
ABCD is ∥gm
AB∥CD
AE∥FC
⇒AB=CD
2
1
AB=
2
1
CD
AE=EC
AECF is ∥gm
In △DQC
F is mid point of DC
FP∥CQ
By converse of mid point theorem P is mid point of DQ
⇒DP=PQ (1)
∴AF and EC bisect BD
In △APB
E is mid point of AB
EQ∥AP
By converse of MPT ( mid point theorem )
Q is mid point of PB
⇒PQ=QB (2)
By (1) and (2)
⇒PQ=QB=DP
AF and EC bisect BD..
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ANSWER
ABCD is ∥gm
AB∥CD
AE∥FC
⇒AB=CD
AECF is ∥gm
In △DQC
F is mid point of DC
FP∥CQ
By converse of mid point theorem P is mid point of DQ
⇒DP=PQ (1)
∴AF and EC bisect BD
In △APB
E is mid point of AB
EQ∥AP
By converse of MPT ( mid point theorem )
Q is mid point of PB
⇒PQ=QB (2)
By (1) and (2)
⇒PQ=QB=DP
AF and EC bisect BD..
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