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Question
If ΔXYZ ~ ΔPQR then `(XY)/(PQ) = (YZ)/(QR)` = ?
Options
`(XZ)/(PR)`
`(XZ)/(PQ)`
`(XZ)/(QR)`
`(YZ)/(PQ)`
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Solution
`bb((XZ)/(PR))`
Explanation:
In ΔXYZ and ΔPQR,
ΔXYZ ~ ΔPQR ...(Given)
`(XY)/(PQ) = (YZ)/(QR) = (XZ)/(PR)` ...[Corresponding sides of similar triangles.]
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In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.
Given: PQ ⊥ BC, AD ⊥ BC
Now, A(ΔPQB) = `1/2 xx square xx square`
A(ΔPBC) = `1/2 xx square xx square`
Therefore,
`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx square xx square)/(1/2 xx square xx square)`
= `square/square`
