Measures of some angles in the figures are given. Prove that `(AP)/(PB

1.	Measures of some angles in the figures are given. Prove that `(AP)/(PB)=(AQ)/(QC)`
Answer» `/_APQ=/_ABC=60^(@)` ………..(Given) `:./_APQ~=/_ABC` `:.` set `PQ\|\|` set BC.(Corresponding angles test for parallel lines )…….1 In `DeltaABC` set `PQ\|\|` side BC …..[From 1] `:.(AP)/(PB)=(AQ)/(QC)`…….. (Basic proportionality theorem)

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Given below are some triangles and lengths of line segments. Identify in which figures, ray PM is the bisector of `/_QPR`.
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As shown in the adjoining figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m, then how long will be the shadow of the bigger pole at the same time?
`DeltaLMN~DeltaPQR`, `9xxA(DeltaPQR)=16xxA(DeltaLMN)`. If `QR=20`, then find `MN`.
As shown in the figures, two poles of height 8m and 4m are perpendicular to the groudn. If the length of shadow smaller pole due to sunlight is 6 m then long will be the shadow of the bigger pole of the same time?
In the adjoining figure, `BP bot AC`, `CQ bot AB`, `A-P-C`, `A-Q-B`. Complete the following activity to Prove `DeltaAPB~DeltaAQC`. In `DeltaAPB` and `DeltaAQC` `/_APB=square^(@)`…….`(1)` `/_AQC=square^(@)`……..`(2)` `:./_APB~=/_AQC`…....(`square`) `:.DeltaAPB~DeltaAQC`......(`square`)
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In the figure seg `PQ||` seg DE, `A(DeltaPQF)=20` units `PF=2DP`,then find `A(square DPQE)` by completing the following activity: Activity: `A(DeltaPQF)=20` sq units, `PF=2DP`. Let us assume `DP=x` `:.PF=2x` `DF=DE+square=square+square=3x` In `DeltaFDE` and `DeltaFPQ`. `/_FDE~=/_square` ..........(Corresponding angles) `/_FED~=/_square` .....(Corresponding angles) `:.DeltaFDE~DeltaFPQ` .....(AA test) `:.(A(DeltaFDE))/(A(DeltaFPQ))=(square)/(square)=((3x)^(2))/((2x)^(2))=9/4` `A(DeltaFDE)=9/4A(DeltaFPQ)=9/4xxsquare=square` `A(squareDPQE)=A(DeltaFDE)-A(DeltaFPQ)` `=square-square` `=square`
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In the adjoining figure, seg `XY||` seg `AC`, IF `3AX=2BX` and `XY=9` then find the length of `AC`.

Measures of some angles in the figures are given. Prove that `(AP)/(PB)=(AQ)/(QC)`

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