Question

21. In AABC, D is the mid-point of BC, prove that
AB2 + CA2 = 2(AD2 + DC2).
a parallelogram.
23. The co-ordinates of a point dividing the line
6.10.
TE
utangle are (5, 1), (1, 5) and (-3,-1). Find the lengths of its medias
, I and (0.3)
22. The vertices of a quadrilateral ABCD are A(3,-2), B(-3, 4), C(1, 8) and D(7,4). Pro
that the line joining the mid-points of the sides AB, BC, CD, DA in the same order for parallelogram
​

Answer 1

Answer:

sorry don't know plzz mark me as

Answer 2

Answer:

Given: In △ABC, ∠B = 90° and D is the mid-point of BC.

To Prove: AC2 = AD2 + 3CD2

Proof:

In △ABD,

AD2 = AB2 + BD2

AB2 = AD2 - BD2 .......(i)

In △ABC,

AC2 = AB2 + BC2

AB2 = AC2- BD2 ........(ii)

Equating (i) and (ii)

AD2 - BD2 = AC2 - BC2

AD2 - BD2 = AC2 - (BD + DC)2

AD2 - BD2 = AC2 - BD2- DC2- 2BDx DC

AD2 = AC2 - DC2 - 2DC2 (DC = BD)

AD2 = AC2 - 3DC2