Question

hola mates...
ABCD is a rhombus show that diagonals AC bisects angle A as well as angle C and diagonal BD bisects Angle B as well as angle D.....

plz don't do on paper plz...
thanks for the help mate
plz be fast.. it's urgent

Answer 1

hey mate.
here's the proof

Answer 2

Hellow Dear Here Is Your Ansr ... !!

Given that ABCD is a Rhombus

So AB = BC = CD = AD.

To Prove : (i) Diagonal AC bisects ∠ A as well as ∠ C.               
 
(ii) Diagonal BD bisects ∠ B as well as ∠ D. 

Proof: (i) ABCD is a rhombus        

AD = CD

∴ ∠ DAC = ∠ DCA ...........(1)  [ Angles opposite to equal sides of a triangle are equal] 

Also, CD || AB  and transversal AC intersects them

∴ ∠ DAC = ∠ BCA ..........…(2)     [Alternate Interior angles]

From (1) and (2)    

∠ DCA = ∠ BCA ⇒ AC bisects ∠ C Similarly AC bisects ∠ A.

(ii)similarly as above, prove that BD bisects ∠ B as well as ∠ D. 

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