Question

Q. 4. PQRS is a parallelogram and PL and RM are
perpendiculars drawn from the vertices P and Rof
the parallelogram on diagonal SQ. Show that
(i) APQL = ARMS (ii) PL = RM.
MIKYS 2014 Board Torm IT
2017 MT
T​

Answer 1

Hello mate..

Here Is Your Answer:

(i) To show,

∆PQL ≅ ∆RMS

PQ = RS (Parallel sides of a parallelogram are equal.)

∠QPL = ∠SRQ (Both angles are given perpendiculars.)

∠PQL = ∠RSM (SQ is a diagonal points L and M lie on it.)

Hence, ∆PQL ≅ ∆RMS [By ASA congruence rule.]

(ii) To prove - PL = RM

By CPCT rule from ∆PQL ≅ ∆RMS.

CPCT - Corresponding parts of Congruent triangles.

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HOPE THIS HELPS YOU..