OP Malhotra Mid-Point and Intercept Theorems Class-9 S.Chand ICSE Maths Ch-9 Notes. We Provide easy notes on it and Step by Step Answer of Exe-9(a), with Chapter Test of OP Malhotra Maths. Visit official Website CISCE for detail information about ICSE Board Class-9.
OP Malhotra Mid-Point and Intercept Theorems Class-9 S.Chand ICSE Maths Ch-9 Notes
Mid-Point Theorem Proof :
If the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides.
Consider the triangle ABC, as shown in the above figure,
Let E and D be the midpoints of the sides AC and AB. Then the line DE is said to be parallel to the side BC, whereas the side DE is half of the side BC; i.e.
DE∥BC
DE = (1/2 * BC).
Mid-Point Theorem Formula :
In Coordinate Geometry, midpoint theorem refers to the midpoint of the line segment. It defines the coordinate points of the midpoint of the line segment can be found by taking the average of the coordinates of the given endpoints. The midpoint formula is used to determine the midpoint between the two given points.
If P1(x1, y1) and P2(x2, y2) are the coordinates of two given endpoints, then the midpoint formula is given as:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
The converse of MidPoint Theorem :
The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.
Line Segment Definition :
A line segment has two endpoints in a line. The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetre (cm), millimetres (mm) or by conventional units like feet or inches.
Practice Questions on Mid-Point Theorem :- Exercise-9(a)
In this chapter, we study all the topics on Mid-Point and Intercept Theorems and do some practice questions also. Here we solve extra practice questions on this chapter for better understanding.
Here is the link for extra practice questions on Mid-Point Theorems :- Chapter Test
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