Formulas for Geometry PDF
Geometry Formulas PDF
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Topics Included in the PDF
- lines and angles
- collinear points
- coplanar points
- Concurrent Lines
- Parallel Lines
- Intersecting Lines
- Line Segment
- Interior of an angle
- Congruent Angles
- The measure of an angle
- Types of angles
- Linear Pair of Angles
- Vertically Opposite Angles
- Triangle and Its Angles
# Topics in the PDF are explained briefly down there:-
Introduction:-In this chapter we will deal with the pure Geometry-related questions. Questions related to the measurement of lengths of lines, areas of surfaces, volumes of solids, etc have been discussed in the chapter ‘Mensuration’.
We shall discuss this chapter under three heads:
1. Lines and Angles
2. Triangle and Its Angles
1.Lines and Angles:
- Point: Point is a basic concept in Geometry. A point is represented by a fine dot made by a sharp pencil on a sheet of paper.
- Plane: The surface of a smooth wall or the surface of a sheet of paper or the surface of a smooth blackboard are examples of a plane
- Line: A geometrical straight line is a set of points and extends endlessly in both directions. To emphasize this point, we use two arrowheads, one at each end.
- Collinear and Coplanar: Three or more points are said to be collinear if there is a line that contains all of them.
- Concurrent Lines: Three or more lines are said to be concurrent if there is a point that lies on all of them.
- Intersecting Lines: Two lines whose intersection is non-empty set are said to be intersecting lines. The common point is called the point of intersection.
- Line Segment: Given two points A and B on a line l, the connected part (segment) of the line with endpoints at A and B, is called the line segment AB.
- Ray: A ray extends infinitely in one direction from any given point. This is exhibited by an arrow. The starting point, say P, of the ray, is called the initial point.
- Interior of an angle: The interior of an angle AOB is the set of all points in its plane which lie on the same side of OA and also on the same side of OB.
2.Triangle and its Angles: A triangle is a closed figure formed by three line segments.
- Congruence of two triangles: Two triangles are congruent if and only if one of them can be made to superpose on the others so as to cover it exactly.
- The similarity of Triangles: For a given correspondence between two triangles, if the corresponding angles are congruent and their corresponding sides are in proportion, then the two triangles are said to be similar
- Side-Angle-Side (SAS) Congruence Criterion: Two triangles are congruent if two sides and
the included angle of one triangle are equal to the corresponding sides and the included angle of the
- Angle-Side-Angle (ASA) Congruence Criterion: Two triangles are congruent if two angles
and the included side of one triangle are equal to the corresponding two angles and the included side
of the other.
- Angle-Angle-Side (AAS) Congruence Criterion: If any two angles and a non-included side of
one triangle are equal to the corresponding angles and side of another, then the two triangles are
- Side-Side-Side (SSS) Congruence Criterion: Two triangles are congruent if the three sides
of one triangle are equal to the corresponding three sides of the other.
- Right Angle-Hypotenuse-Side (RHS) Congruence Criterion: Two right triangles are congruent
if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one
side of the other.
3. Circle: A circle is a closed plane figure consisting of all those points of the plane which are at a constant
distance from a fixed point in the plane
- Circular disc: The set of all points lying inside and on the circle is called a circular disc with
center O and radius r.
- Concentric circles: Circles having the same center but with different radii are said to be concentric
- Arc of a circle: Any two points, say A and B, of a circle, divide the circle into two parts called the
arcs of the circle. If the two parts are unequal, the smaller part is called the minor arc and the larger
one is called the major arc.
- Semicircle: If any two points A and B divide the circle into two equal parts then each part is
called a semicircle.
- The degree measure of an arc: The degree measure of a minor arc is the measure of the central
angle containing the arc. And that of a major arc is 360° minus the degree measure of the corresponding
- Secant: A secant is a line, which intersects the circle in two distinct points.
- Chord: A line segment joining any two points of a circle is called a chord of the circle.
- Diameter (d): A chord passing through the center of a circle is called its diameter. A diameter is
the longest chord of a circle.
- A segment of a circle: Let AB be a chord of the circle. Then AB divides the region enclosed by the
circle (ie the circular disc) into two parts. Each of these parts is called a segment of the circle.
Formulas for Geometry PDF
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