Question

6 the given figure o is the midpoint of each of the line segment a b and CD prove that AC is equal to BD and ac parallel BC

Answer 1

$\huge \sf\green{Solution : }$

In triangles AOC and BOD, we have

AO = BO (O, the midpoint of AB) ;

∠AOC=∠BOD, (vertically opposite angles);

CO=OD, (O, the midpoint of CD)

So by SAS postulate we have

△AOC≅△BOD.

Hence, AC = BD, as they are corresponding parts of congruent triangles.

$\sf \blue{Hope \: it \: helps \: you !!}$

Answer 2

Answer:

In triangles AOC and BOD, we have

AO = BO (O, the midpoint of AB) ;

∠AOC=∠BOD, (vertically opposite angles);

CO=OD, (O, the midpoint of CD)

So by SAS postulate we have

△AOC≅△BOD.

Hence, AC = BD, as they are corresponding parts of congruent triangles.