Question

If D is the mid point of the hypotenuse AC of a right angled ∆ABC. Prove that BD= ½AC


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Answer 1

Explanation:

In ∆ ABC and ∆ ECB,

angle ABC = angle ECB______from construction

seg AB = seg CE_________opposites sides

seg BC = seg BC ______common side

now, ∆ABC ~ ∆ ECB

SegAC = seg BE____ hypotenuse of congruent

triangles__(1)

BD = DE____given___(2)

so,BD + DE = BE

BD + BD = BE___from 2

BD = 1 BE

2

now, BD = 1 AC __from 1

2

hence it is prove