How many equal intercepts are formed when 3 transversals intersect 3 parallel lines ?
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The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally.
On extending the tranversals l1 and l2, they join at A. join the other two ends with line BC , forming a triangle − △ABC
∴
BC
AB
=
QR
PQ
Given
BC
AB
=
1
1
∴
QR
PQ
=
1
1
.
This can also be solved as below:
If three parallel lines are intercepted by 2 transversals, in such a way that the two intercepts on one traversal are equal, then the intercepts formed by the other transversal are also equal.
Given
BC
AB
=
1
1
⟹ AB=BC
∴
QR
PQ
=
1
1
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