Question

if ABCD is a rhombus then AC²+ BD² is equal to

Answer 1

hey guy !!!!!!!
yr question is seems to be incomplete

Answer 2

SOCRATIC

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If ABCD is a rhombus, how do you prove that 4BC2=AC2+BD2?

Geometry  Quadrilaterals

1 Answer



CW

Oct 12, 2016

Answer:

see explanation.

Explanation:



Rhombus properties :

1) The sides of a rhombus are all congruent (the same length.) AB=BC=CD=DA=a

2) Opposite angles of a rhombus are congruent (the same size and measure.)
∠BAD=∠BCD=y,and∠ABC=∠ADC=x

3) The intersection of the diagonals of a rhombus form 90 degree (right) angles. This means that they are perpendicular. 
∠AOB=∠BOC=∠COD=∠DOA=90∘

4) The diagonals of a rhombus bisect each other. This means that they cut each other in half.
BO=OD=12BD=m,andAO=OC=12AC=n

5) Adjacent sides of a rhombus are supplementary. This means that their measures add up to 180 degrees.
x+y=180∘

Now back to our question.

In ΔBOC,BC2=BO2+OC2
Since BO=12BD,andOC=12AC

⇒BC2=(12BD)2+(12AC)2

⇒BC2=14(BD)2+14(AC)2

⇒BC2=14(BD2+AC2)

⇒4BC2=AC2+BD2