Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Management
  • Two sides AB and BC, and the median AD of ABC are correspondingly equal to the two sides PQ and QR, and the median PM of

Two sides AB and BC, and the median AD of \DeltaABC are correspondingly equal to the two sides PQ and QR, and the median PM of \DeltaPQR. Then,

Option: 1

\angle A B C=\angle P Q R


Option: 2

BD=QM


Option: 3

\triangle A B C \cong \Delta P Q R


Option: 4

All of the above


Answers (1)

best_answer

\\\text{In } \triangle A B D\text{ and }\triangle P Q M,\text{ we have} \\\\A B=P Q \quad(\text { given }) \\ \\B D=Q M \quad\left[\because B C=Q R \Rightarrow \frac{1}{2} B C=\frac{1}{2} Q R \Rightarrow B D=Q M\right] \\\\\text { med. } A D=\text { med. } P M \quad(\text { given })

\\\therefore \quad \triangle A B D \cong \triangle P Q R \quad \text { (SSS-criteria) } \\\\ \therefore \quad \angle A B D=\angle P Q M \quad( \text { c.p.c.t.) } \\\\ \Rightarrow \quad \angle A B C=\angle P Q R\\ \\\text{Now, in } \triangle A B C\text{ and } \triangle P Q R,\text{ we have} \\\\ A B=P Q \quad(\text { given })

\\ \angle A B C=\angle P Q R \quad \text { (proved above) } \\ \\B C=Q R \quad \text { (given). } \\ \\\therefore \quad \triangle A B C \cong \Delta P Q R \quad \text { (SAS-criteria). }

 

Posted by

HARSH KANKARIA

View full answer

Similar Questions

Trending Articles/News

anam-khan

CAT 2026 application process begins at iimcat.ac.in; MBA entrance exam on November 29
anam-khan

CAT Application Form 2026 LIVE: Registration opens for B-schools; application fee, syllabus, dates
anam-khan

CAT 2026 on November 29; what changes this year?

Latest Question