Question

ABCD is parallelogram. If diagonal AC
bisects angle A, then prove that
(i) AC bisects cel
(ii) ABCD is a rhombus
(iii) ACis perpendicular to BD​

Answer 1

Answer:AC bisect angle A

Angle DCA equals to angle BAC

ANGLE DAC equals ACB (BECAUSR THEY ARE ALTERNATE INTERIOR ANGLES)

THEREFORE ANGLE DCA EQUALS TO ANGLE BCA

SO, AC BISECTS THE ANGLE C ALSO

ANGLE DCA EQUALS TO ANGLE BCA( PROVED)

THEN, DA EQUALS TO AB ( BECAUSE SIDES OPPOSITE TO EQUAL ANGLE ARE EQUAL)

SIMILARLY, DC EQUALS TO BC

SINCE, ALL THE SIDES OF PARALLELOGRAM ABCD ARE EQUAL , THEN IT IS A RHOMBUS

Step-by-step explanation: