wiz-icon
MyQuestionIcon
MyQuestionIcon
10
You visited us 10 times! Enjoying our articles? Unlock Full Access!
Question

In the alongside diagram, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B.
State whether true or false for the following equation
PQ = CD

194912_363c88df670c4c2aa03393d804897099.png

A
True
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
False
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A True
Let O be the point of intersection of the angular bisectors AP, and QB

We know that,
1) Angular bisectors intersect at 90.
2) Angular bisectors bisect each other, i.e., AO=OP and BO=OQ

Join QP, to form POQ

Consider AOB and POQ,

AO=OP
AOB=POQ=90
BO=OQ

The two triangles are congruent. Hence the side AB and QP must be equal. Hence, parallel.

We know that, in parallelogram ABCD,

AB=CD and ABCD

Hence, CD=QP and CDQP. Proved.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Criteria for Congruency
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon