Login

ABCD is a parallelogram and AP and CQ are perpendicular from vertices A and C on the diagonal BD. show that AP=CQ.

Given that: ABCD is a parallelogram

To Prove : AP = CQ

 

Proof:

In Δ APB and Δ CQD

∠APB = ∠CQD  [ EACH RIGHT ANGLE ]

 AB = CD  (opposite sides of parallelogram ABCD)

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

So, Δ APB is congruent to Δ CQD  [ AAS ]

⇒  AP = CQ  [CPCT]

  • 49
View Full Answer

Given: ABCD is a parallelogram. AP and Bd are perpendicular to BD!

To show: AP= CQ

Proof: Consider triangles APB and CQD,

AB = CD (Opp. sides are equal)

angle APB = angle CQB = 90 degree (Given)

angle CDP = angle PBA ( Alternate interior angles, AB is parallel to CD)

Therefore, By SAS congruence,

triangle APB is congruent to tiangle CQD.

By CPCT,

AP =CQ!

Hope this helps!!!

  • 7
What are you looking for?