Question

EFGH is a rhombus. Show that EG bisects angle E and angle G both.​

Answer 1

Step-by-step explanation:

Here, EFGH is rhombus and EG is diagonal.

In △EFG,

⇒  EF=FG       [ Sides of rhombus are equal ]

⇒  ∠2=∠4      [ Angles opposite to equal sides are equal ] ----- ( 1 )

Now, EH∥FG and EG is transversal.           [ Opposite sides of rhombus are parallel ]

⇒  ∠1=∠4           [ Alternate angles ]    ----- ( 2 )

From ( 1 ) and ( 2 ),

⇒  ∠1=∠2

⇒  EG bisects ∠E

Now, EF∥GH and EG is transversal.

⇒  ∠2=∠3         [ Alternate angles ]      ----- ( 3 )

From ( 1 ) and ( 3 )

⇒  ∠4=∠3

⇒  EG bisects ∠G

Hence, EG bisects ∠E and ∠G

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