Question

ABCD is a rhombus show that diagonal AC bisect angle A as well as angle C and diagonal BD bisects angles well as angle D ​

Answer 1

Answer:

ABCD is a rhombus.

AB = BC = CD = AD

Also, AB || CD and AD || BC

Now, AD = CD

∠1 =∠2

Also,  CD || AB

and AC is AC transversal.

∠1 =∠3

From (1) and (2), we have

∠2 =∠3 and ∠1 =∠4

AC bisects ∠C as well as ∠A.

Similarly, we prove that BD bisects ∠B as well as ∠D.

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