Transversals t_{1} and t_{2} to l_{1} paralle | vedclass

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(A) According to the Intercept Theorem (or Thales's Theorem for parallel lines),if three or more parallel lines are intersected by two transversals,th

Vedclass · Accepted Answer

$6.3$

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(A) According to the Intercept Theorem (or Thales's Theorem for parallel lines),if three or more parallel lines are intersected by two transversals,then they cut off the transversals proportionally.Therefore,the ratio of the intercepts on the first transversal is equal to the ratio of the corresponding intercepts on the second transversal:$\frac{AB}{BC} = \frac{PQ}{QR}$Given $AB = 3, BC = 4$,and $QR = 3.6$,we substitute these values into the equation:$\frac{3}{4} = \frac{PQ}{3.6}$$PQ = \frac{3 	imes 3.6}{4}$$PQ = 3 	imes 0.9 = 2.7$We need to find $PR$,where $PR = PQ + QR$.$PR = 2.7 + 3.6 = 6.3$Thus,the length of $PR$ is $6.3$.

Transversals $t_{1}$ and $t_{2}$ to $l_{1} \parallel l_{2} \parallel l_{3}$ intersect them at $A, B, C$ and $P, Q, R$ respectively. If $AB = 3, BC = 4$ and $QR = 3.6$,find $PR$.

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