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State whether the following statement is true or false:

If in a parallelogram JUMP, $L$ and $N$ are points respectively on $JU$ and $MP, JL = NM$ , then $LN$ and UP bisect each other.

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True

False

answer is A.

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Detailed Solution

Given,
In parallelogram JUMP,

JL = NM

where

L

and

N

are points respectively on

JU

and MP.

NM and JL are equal

⇒

LU and PN are equal… (1)
LN and UP intersect at point O.
In

Δ O P N and Δ O U L,

∠ N P O = ∠ L U O

[

M P ∥ U L

with UP as transversal, Alternate angles]

P N = U L

[From (1)]

∠ P N O = ∠ O L U

[

M P ∥ U L

with NL as transversal, Alternate angles]

∴ Δ O P N ≅ Δ O U L

[By ASA test]
By CPCT,
OP=OU and ON=OL.
Thus, LN and UP bisect each other and the given statement is true.
Hence, the correct option is 1.

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