Notifications
Clear all
Triangles
1
Posts
2
Users
0
Likes
508
Views
0
12/07/2021 12:01 pm
Topic starter
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see Figure). Show that:
(i) ΔABM ΔPQN
(ii) ΔABC ΔPQR
1 Answer
0
12/07/2021 12:03 pm
Given parameters are:
AB = PQ,
BC = QR and
AM = PN
(i) 1/2 BC = BM and 1/2 QR = QN (Since AM and PN are medians)
BC = QR
1/2 BC = 1/2 QR
⇒ BM = QN
In ΔABM and ΔPQN,
AM = PN and AB = PQ (As given in the question)
BM = QN (Already proved)
∴ ΔABM ΔPQN by SSS congruency.
(ii) In ΔABC and ΔPQR,
AB = PQ and BC = QR (As given in the question)
ABC = PQR (by CPCT)
So, ΔABC ΔPQR by SAS congruency.