Question

P is the mid-point of side AB to a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. Then BR is equal to ______.

A
BQ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
12BQ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2BQ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 2BQIn △ABR, P is the mid-point of AB and DP||BR∴D is the mid-point of AR .....(Converse of mid-point theorem).Then, AR=2AD⟹ AR=2BC (Opposite sides of parallelogram are equal, i.e. AD=BC)⟹ AD=BC. Also, D is the mid-point of AR and DQ||AB ....(Since, ABCD is parallelogram)Then, Q is the mid-point of DC ....(Converse of mid-point theorem)∴BR=2BQ.Hence, option C is correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
The Mid-Point Theorem
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program