Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices a and c on diagonal bd. show that

i)△ APB ≅ △ CQD
ii)AP = CQ

Answer 1

Ans....

Please mark me Brilliant answer..

Answer 2

Answer:

(i) Given that , ABCD is a parallelogram

with AD is perpendicular to BD

and CQ is perpendicular to BD

To prove--- Triangle APB = Triangle CQD

Proof - now, AB || DC ( opposite sides of parallelogram)

and transversal BD

/_ ABP = /_ CDQ ( Alternative angle).......eq. 1

in Triangle ABP and CDQ

/_ APB = CDQ ( both 90°)

/_ ABP = /_ CDQ ( from eq. 1)

AB = CD ( opposite side of Triangle is equal)

Therefore, Triangle APB = Triangle CQD (by AAS)

Step-by-step explanation:

(ii) AP = CQ [ C.P.C.T ]