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

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

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$10.4$

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(D) According to the Intercept Theorem (or Thales's Theorem for parallel lines),if three or more parallel lines are intersected by two transversals,then the intercepts made on the transversals are proportional.Therefore,$\frac{AB}{BC} = \frac{PQ}{QR}$.Given values are $AB = 5$,$BC = 8$,and $PQ = 6.5$.Substituting these values into the proportion: $\frac{5}{8} = \frac{6.5}{QR}$.Cross-multiplying gives: $5 	imes QR = 8 	imes 6.5$.$5 	imes QR = 52$.$QR = \frac{52}{5} = 10.4$.Thus,the length of $QR$ is $10.4$.

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 $AB = 5$,$BC = 8$ and $PQ = 6.5$,find $QR$.

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