Q. (1) In fig (10).9(2) It is given that AB = CD and AD = BC. Prove that ΔADC≅ΔCBA.
Given that in the figure AB = CD and AD = BC.
We have to prove ΔADC≅ΔCBA
Consider Δ ADC and Δ CBA.
AB = CD [Given]
BC = AD [Given]
And AC = AC [Common side]
So, by SSS congruence criterion, we have
Q. (2) In a Δ PQR. IF PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP respectively. Prove that LN = MN.
Sol: Given that in Δ PQR, PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP respectively
We have to prove LN = MN.
Join L and M, M and N, N and L
We have PL = LQ, QM = MR and RN = NP
[Since, L, M and N are mid-points of Pp. QR and RP respectively]
And also PQ = QR
MN ∥ PQ and MN =
Similarly, we have
LN ∥ QR and LN = (1/2)QR
From equation (i), (ii) and (iii), we have
PL = LQ = QM = MR = MN = LN
LN = MN