Question

ABCD is a rhombus so that the diagonal BD bisect angle B and angle d and diagonal AC bisect angle A and angle c​

Answer 1

Step-by-step explanation

In △ABD and △BCD,

AB=BC ....Sides of a rhombus

AD=CD ....Sides of a rhombus

AC=AC ....Common side

△ABD≅△BCD ...SSS test of congruence

∴∠ABD=∠CBD ....C.P.C.T.

∴∠ADB=∠CDB ....C.P.C.T.

So, Diagonal BD bisects ∠B and ∠D of the rhombus ABCD.

Similarly we can prove,

△ABC≅△ADC

∴∠BAC=∠DAC ....C.P.C.T.

∴∠BCA=∠DCA ....C.P.C.T

So, Diagonal AC bisects ∠A and ∠C of the rhombus ABCD.