Question

the ratio of the intercepts made on a traversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines. "this property is known as ​

Answer 1

Answer: Property of intercepts made by three parallel lines on a transversal $\frac{AB}{BC} =\frac{PQ}{QR}$.

Step-by-step explanation: As the ratio of the intercepts made on a transversal by three parallel lines is equal to the corresponding intercepts made on any other transversal by the same parallel lines.

As given that Line l ║Line m║Line n

As t1 and t2 are transversals. Transversal t1 intersects the line in points A, B, C and t2 intersect the line in point P, Q, and R.

$\frac{AB}{BC} =\frac{PQ}{QR}$

As draw seg PC, which intersects line m at point D.

In triangle ACP, BD║AP

As therefore, $\frac{AB}{BC} =\frac{PD}{DC} .....(1) (B.P.T)$

As in triangle CPR, DQ║CR,

So, therefore, $\frac{PD}{DC} =\frac{PD}{QR} .....(2) (B.P.T)$

Now from equations (1) and (2)

Therefore$\frac{AB}{BC} =\frac{PD}{DC} =\frac{PQ}{QR}$,

$\frac{AB}{BC} =\frac{PQ}{QR}$.

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Answer 2

Answer:

the ratio of the intercepts made on a traversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines. "this property is known as the ratio of the intercepts made on a traversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines. "this property is known as