Question

3.
In the given figures, BD and YE are the medians.
Find the value of YZ.(State the reasons)
​

Answer 1

Solution :-

In ∆ABD and ∆XYQ we have,

→ AB = XY (given)

→ BD = YQ (given)

→ AD = XQ (given)

so,

→ ∆ABD ~ ∆XYQ {By SSS similarity .}

then,

→ ∠BAD = ∠YXQ { By CPCT .}

or,

→ ∠BAC = ∠YXZ --------- Eqn.(1)

also,

→ AB/XY = AD/XQ

since D and Q are medians .

→ AB/XY = (1/2)AC/(1/2)XZ

→ AB/XY = AC/XZ -------- Eqn.(2)

then from Eqn.(1) and Eqn.(2) we get,

→ ∆ABC ~ ∆XYZ { By SAS similarity. }

therefore,

→ BC = YZ { By CPCT.}

hence,

→ YZ = 5 cm (Ans.)

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