Question

ABCD is a parallelogram if the diagonal AC bisects angle A then prove that AC bisects angle C ABCD is a rhombus ac perpendicular bd

Answer 1

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

Answer 2

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