Which are the ratio of intercept?
Property of Intercepts made by three parallel lines on a transversal. Statement: The ratio of the intercepts made on the transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal of the same parallel line.
How do you prove the equal intercept theorem?
If there are three or more parallel lines and the intercepts made by them on the transversal are equal, the corresponding intercepts on any other transversal are also equal. Given: Lines l,m and n such that l||m||n, p is a transversal that cuts l,m,ninA,B,C respectively such that AB=BC.
What is the 3 parallel lines theorem?
The three parallel lines theorem is another theorem that provides a ratio between line segments created by a transversal of parallel lines, similar to the Intercept Theorem.
What is ratio theorem?
This theorem is very useful for finding the coordinates of a point that divides a line into a certain ratio. If P is any point on a line AB, and if, a, b and p are the position vectors of A, B and P respectively, then. p = λa + μb. and the ratio AP : PB =μ: λ for the constants λ and μ such that μ + λ =1.
What is intercept and transversal?
The line segment PQ is called the intercept made on the transversal XY by the lines L1 and L2. If a transversal makes equal intercepts on three or more parallel lines then any other transversal cutting them will also make equal intercepts.
What is the equal intercept theorem?
The theorem states if a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts. So any line passing through them, the intercept made by l-m on the line is twice the intercept made by m-n. …
What is true about transversals that cross three or more parallel lines?
Similarly, three or more parallel lines also separate transversals into proportional parts. If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
What can you conclude about the ratio of line segments if three parallel lines are intersected by two transversals?
Theorem: If three or more parallel lines are cut by two transversals, then they divide the transversals proportionally.
When three or more parallel lines cut two transversals they separate the transversals into?
proportional parts
Similarly, three or more parallel lines also separate transversals into proportional parts. If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
What theorem states that if three parallel lines have two Tranversals Then they divide the transversals proportionally?
Parallel Transverals
Parallel Transverals Theorem: If three or more parallel lines are cut by two transversals, then they divide the transversals proportionally.
Is the ratio of the intercepts made on the transversal by three parallel lines equal?
Statement: The ratio of the intercepts made on the transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal of the same parallel line.
Which is a statement of the equal intercept theorem?
Statement: The ratio of the intercepts made on the transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal of the same parallel line. Consider the above figure, line l, m, and n are parallel to each other.
Is the BPT a converse of any theorem?
Hence Proved. The BPT also has a converse which states, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. (Note: A converse of any theorem is just a reverse of the original theorem, just like we have active and passive voices in English.)