Question

In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively.
Prove that: PR = QR

Answer 1

In ΔABC,
AB = AC
⇒ `1/2 "AB" = 1/2"AC"`
⇒ AP = AQ                     ...(i)[ Since P and Q are mid - points ]

In ΔBCA,
PR = `1/2"AC"`                 ...[ PR is line joining the mid - points of AB and BC ]
⇒ PR = AQ                      ...(ii)

In ΔCAB,
QR = `1/2"AB"`                 ...[ QR is line joining the mid - points of AC and BC ]
⇒ QR = AP                       …(iii)
From (i), (ii) and (iii)
PR = QR.