Question

Diagonal AC of a parallelogram ABCD bisects angleA. show that:

(i) it bisects angleC also
(ii)ABCD is rhombus

Answer 1

HEY.....

HERE IS UR ANSWER...

ABCD IS A PARALLELOGRAM

THEREFORE ANGLE DCA = ANGLE CAM AND

ANGLE DAC = ANGLE ACB
[ ALTERNATE ANGLES]

BUT ANGLE DAC = ANGLE CAB

THEREFORE ANGLE DCA = ACB
SO AC BISECT ANGLE C ALSO..


NOW ANGLE CAB = DCA AND
ANGLE CAM =DAC

THEREFORE ANGLE DCA = ANGLE DAC

SIDES OPP. TO EQUAL ANGLES ARE EQUAL ...

THEREFORE AD= DC


NOW IF IN A PARALLELOGRAM ADJACENT SIDES ARE EQUAL THEN IT IS RHOMBUS...