Q. 64.3( 21 Votes )

ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that

(i) Δ APB Δ CQD

(ii) AP = CQ



Answer :

Given:- ABCD is parallelogram


Formula used :- AAS property


If 2 angles and any one side is are equal in both triangle


Then both triangles are congruent


Solution:-


In Δ APB and Δ CQD


CQD= APB=90°


If ABCD is a parallelogram


CDB= DBA [alternate angles as DC||AB]


AB=DC [opposite sides of parallelogram are equal]


By AAS property


Δ APB Δ CQD


If Δ APB Δ CQD


Then


AP=CQ


Conclusion:-


In parallelogram ABCD; Δ APB Δ CQD


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Critical Thinking Problems on QuadrilateralsCritical Thinking Problems on QuadrilateralsCritical Thinking Problems on Quadrilaterals44 mins
Quiz | Properties of ParallelogramQuiz | Properties of ParallelogramQuiz | Properties of Parallelogram31 mins
Quiz | Basics of QuadrilateralsQuiz | Basics of QuadrilateralsQuiz | Basics of Quadrilaterals36 mins
RD Sharma |  Extra Qs. of Cyclic QuadrilateralsRD Sharma |  Extra Qs. of Cyclic QuadrilateralsRD Sharma | Extra Qs. of Cyclic Quadrilaterals31 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :