Question
Mon August 06, 2012 By: Kishan Chaudhary
 

if the diagonal BD of a quadrilateral ABCD bisect both angle b and d show that AB upon BC equals too AD upon CDA

Expert Reply
Mon August 06, 2012

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)

So, triangles ABD and CBD are similar, by AA similarity

Since, corresponding sides of similar traingles are proportional, we have:

AB/BC = AD/CD

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