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ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ - Mathematics

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ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that

(i) ΔAPB ≅ ΔCQD

(ii) AP = CQ

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Solution

(i) In ΔAPB and ΔCQD,

∠APB = ∠CQD (Each 90°)

AB = CD (Opposite sides of parallelogram ABCD)

∠ABP = ∠CDQ (Alternate interior angles for AB || CD)

∴ ΔAPB ≅ ΔCQD (By AAS congruency)

 

(ii) By using the above result

ΔAPB ≅ ΔCQD, we obtain

AP = CQ (By CPCT)

Concept: Another Condition for a Quadrilateral to Be a Parallelogram
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APPEARS IN

NCERT Class 9 Maths
Chapter 8 Quadrilaterals
Exercise 8.1 | Q 10 | Page 147

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