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When three parallel lines are cut by two transversals and the intercepts made by the first transversal are in the ratio 3:5, then the intercepts made by the second transversal are in the ratio________.
3:5
9:25
3:2
1:1
3:5
According to the Intercept Theorem (Thales's Theorem for parallel lines), the ratio of the corresponding segments cut by parallel lines is constant across all transversals. Therefore, the ratio remains 3 : 5.
There are three parallel lines cut by two transversals. The ratio of the intercepts on the first transversal is 3 : 5.
baтАЛ=dcтАЛ
According to the Intercept Theorem (Thales's Theorem for parallel lines), the ratio of the corresponding segments cut by parallel lines is constant across all transversals. Therefore, the ratio remains 3 : 5.
Students might mistakenly square the ratio (9 : 25) as they would for areas of similar triangles, but this property applies only to linear segments.
Understanding the Intercept Theorem
The Intercept Theorem states that if three or more parallel lines are intersected by two transversals, then the parallel lines cut off proportional segments on the transversals.
Ratio1тАЛ=Ratio2тАЛ
Applying the Property
If the ratio of the intercepts on the first transversal is 3:5, then the corresponding segments on the second transversal must also be in the same proportion 3:5.
3:5=3:5
A is correct because the Intercept Theorem states that segments created by parallel lines on any transversal are proportional to the corresponding segments on any other transversal.
This is a direct application of Thales's Theorem; remember that proportionality holds for linear intercepts but ratios of areas involve the square of the scale factor.
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