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प्रश्न
In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.
उत्तर
Given: PM = 15, PQ = 25, PR = 20 and NR = 8
PQ = PM + MQ
25 = 15 + MQ
⇒ MQ = 25 - 15 = 10
⇒ MQ = 10
PR = PN + NR
20 = PN + 8
⇒ PN = 20 - 8
⇒ PN = 12
`"PM"/"MQ" = 15/10 = 3/2`
`"PN"/"NR" = 12/8 = 3/2`
In ΔPQR,
`"PM"/"MQ" = "PN"/"NR"`
By converse of basic proportionality theorem, NM is parallel to side RQ or NM || RQ.
संबंधित प्रश्न
In trapezium ABCD, side AB || side PQ || side DC, AP = 15, PD = 12, QC = 14, Find BQ.
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AB = 60, BC = 70, CD = 80, PS = 280 then find PQ, QR, and RS.
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Activity: 2AX = 3BX
∴ `"AX"/"BX" = square/square`
`("AX" +"BX")/"BX" = (square + square)/square` ...(by componendo)
`"AB"/"BX" = square/square` ...(I)
ΔBCA ~ ΔBYX ...`square` test of similarity,
∴ `"BA"/"BX" = "AC"/"XY"` ...(corresponding sides of similar triangles)
∴ `square/square = "AC"/9`
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In the above figure, line AB || line CD || line EF, line l, and line m are its transversals. If AC = 6, CE = 9. BD = 8, then complete the following activity to find DF.
Activity :
`"AC"/"" = ""/"DF"` (Property of three parallel lines and their transversal)
∴ `6/9 = ""/"DF"`
∴ `"DF" = "___"`
