What is intercept theorem for Class 9?
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.
What is intercept theorem in math?
The intercept theorem, also known as Thales’s theorem, basic proportionality theorem or side splitter theorem is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. …
How do you prove the intercept theorem?
If a transversal makes equal intercepts on three or more parallel lines then any other transversal cutting them will also make equal intercepts.
- Given: Let there be three straight lines L1, L2, and L3 such that L1 ∥ L2 ∥ L3.
- To Prove: KM = MN.
- Construction: Join PN which cuts the L2 at O.
- Proof:
How do you prove Converse mid point theorem?
Proof. Let E and F be the midpoints of AC and AB respectively, and G the intersection of the medians BE and CF. Construct the parallel through C to BE, and extend AG to intersect BC at D, and this parallel at H. By the converse of the midpoint theorem, G is the midpoint of AH, and HC = 2 · GE.
What is BPT in math?
Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
What’s a Y intercept?
The y -intercept of a graph is the point where the graph crosses the y -axis. When the equation of a line is written in slope-intercept form ( y=mx+b ), the y -intercept b can be read immediately from the equation. Example 1: The graph of y=34x−2 has its y -intercept at −2 .
Who derived Heron’s formula?
Heron of Alexandria
Heron’s formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides.
What is AAA similarity criterion?
\[AAA\] – Similarity: If all the corresponding angles of two triangles are equal , then the two triangles are said to be similar .
Who discovered mid point theorem?
Archimedes’ Midpoint Theorem — from Wolfram MathWorld.
Is there any converse of intercept theorem?
theorem. It states that “if two intersecting lines are cut by parallel lines, the line segments cut by the parallel lines from one of the lines are proportional to the corresponding line segments cut by them from the other line”. Similarly, the converse of the intercept theorem states (see Fig.
What is the converse of BPT?
According to this theorem, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
