Question

If the diagonal BD of quadrilateral ABCD bisects angle B and angle D probe that AB/BC=AD/CD

Answer 1

Given: diagonal BD bisects angle B and angle D

To prove: AB/BC= AD/CD

Proof: in triangle ABD and triangle CBD

angle ABD= angle CBD  (BD bisects angle B)

angle ADB= angle CDB  ( BD bisects angle D)

therefore,   triangle ABD similar to triangle CBD  (AA)

so,  AB/BC = AD/CD  (cpst, i.e., coressponding parts of similar triangle)

hence proved.........

Answer 2

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