Question

In the given figure,AB=BC and angle ABO = angle CBO, then prove that angle DAB = angle ECB.​

Answer 1

Answer:

You can solve this by exterior angle property

Step-by-step explanation:

Answer 2

∠DAB = ∠ECB Hence, Proved

GIVEN

AB=BC and ∠ABO = ∠CBO

TO FIND

∠DAB = ∠ECB

SOLUTION

We can simply solve the above problem as follows;

ΔABO and ΔCBO

AB = CB (Given)

∠ABO = ∠CBO (Given) (Equation 1)

OB = OB (Common)

By Side-Angle-Side criterion

ΔABO ≈ ΔCBO

Therefore,

∠AOB =∠COB (By CPCT) (Equation 2)

We know that, Exterior angle is equal to the sum two interior angle of the triangle.

Therefore,

∠DAB = ∠AOB + ∠ABO

Also,

∠ ECB = ∠COB + ∠CBO

Form Equation 1 and 2

∠AOB + ∠ABO = ∠COB + ∠CBO

So,

∠DAB = ∠ECB Hence, Proved

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