STD IX – GEOMETRY – (Online)

TRIANGLES

A triangle is a polygon with three edges and three vertices. It is one of the

basic shapes in geometry. Basically, it is a closed figure bounded by 3-line segments, it is denoted by Δ.

ISOSCELES TRIANGLES

An Isosceles triangle is a triangle in which two sides have the same length, the two angles opposite to the sides of equal length or the base angles are equal.

INEQUALITIES

The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. If a, b, and c are the lengths of the sides of the triangle, with no side being greater than c, then the triangle inequality states that: c ≤ a + b.

MID-POINT THEOREM AND ITS CONVERSE

The mid-point of the line segment is the geometric centre of the line segment. Mid-point of a line segment divides it into two equal halves.

Midpoint theorem plays a vital role in mathematics. Given a triangle, if we connect two sides with a line segment, and this line segment joins each of the two sides at the centers, or midpoints of each side, we can know two very important aspects about the triangle and the relationships between the sides. We shall see this in mid point theorem and converse of midpoint theorem.

PYTHAGORAS THEOREM

Right angled triangle

A right angled triangle has only one right angle and the other two angles are acute

∠B = 900

The side opposite to the right angle is called the hypotenuse

Side AC is the hypotenuse and it is the largest side in the triangle

RECTILINEAR FIGURES

Rectilinear means along a straight line or in a straight line or forming a straight line. Basically, it is a plane figure bounded by line segments.

CONSTRUCTION OF POLYGONS

Recall in Geometry, When you’re asked to construct, it’s time to break out that compass and straight edge! In this topic, we shall learn how to construct triangles no matter what you’re given.

AREA THEOREM

Parallelograms on the same base and between the same parallels are equal in area

The area of a parallelogram is equal to the area of the rectangle on the same base and of the same altitude, i.e., between the same parallels.

CIRCLE

Chord Properties of Circles

A circle is a locus of a point which moves in a plane in such a way that its distance from a fixed point in the same plane always remains constant.

Arc and its types

An arc is a part of the circumference of a circle

The smaller arc is called the minor arc

The larger arc is called the major arc