Question

ABCD is a rhombus .Show that diagonal AC bisects angle A as well as angle C and diagonal BD bisects angle B as well as angle D

Answer 1

ABCD is a rhombus
so, it's all side are equal.
Take a triangle ABC
in which AB=AC
AngleACB=AngleBAC. Equation 1
In triangle ADC
AD=CD
so, angle DCA=Angle DAC. Equation2
from 1 and 2
we get,
AC bisect angle A and angle B
similarly,
BD bisect angle C and angle D

Answer 2

Answer:

Given, ABCD is a rhombus.

So, AB=BC=CD=AD

To prove:

<BAC=<DAC and <DCA =<BCA

Solution :In triangles ADC AND ABC,

AB =AD(given)

CD= CB (given)

AC is common.

So,triangles ADC=ABC.

So,BY CPCT

<BAC=<DAC

<DCA=<BCA