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Math Resources - STD 9 (CBSE Board)

 
 


 


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शिष्यवृत्ती परीक्षांच्या अभ्यासासाठी सीडी-रॉम (CD for the preparation of scholarship exams)


 
 

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Theorems - Quadrilaterals

Quadrilaterals : Introduction

Quadrilaterals : Introduction 2

Types of quadrilaterals  
Theorem 1 - A diagonal of a parallelogram divides it into two congruent triangles. Theorem 2 - In a parallelogram, opposite sides are equal.
Theorem 3 - If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Theorem 4 - In a parallelogram, opposite sides are equal.
Theorem 5 - If each pair of opposite angles in a quadrilateral is equal, then it is a parallelogram. Theorem 6 - The diagonals of a parallelogram bisect each other.
Theorem 7 - If diagonals of a quadrilateral bisect each other, then it is a parallelogram. Theorem 8 - If one pair of opposite sides of a quadrilateral is equal and parallel, then it is a parallelogram.
Theorem 9 - Mid point theorem : the line joining midpoints of two sides of a triangle is parallel to the third side. Theorem 10 - The line drawn from midpoint of one side of a triangle, parallel to another side, bisects the third side.

Theorems - Circles

If two arcs of a circle (or of congruent circles) are congruent, then corresponding chords are equal. If two chords of a circle (or of congruent circles) a4re equal, then their corresponding arcs (minor, major or semicircular) are congruent.
The perpendicular from the center of a circle to a chord bisects the chord. The line joining the center of a circle to the mid-point of a chord is perpendicular to the chord
There is one and only one circle passing through three non-collinear points. Two chords AB and AC of a circle are equal. The center of the circle lies on the angle bisector of angle BAC.
If two chords AB and AC of a circle with center O are such that the center O lies on the angle bisector of angle BAC, two chords AB and AC are equal. If two circles intersect in two points, the line through the centers is the perpendicular bisector of the common chord.
Equal chords of a circle are equidistant from the center. Chords of a circle which are equidistant from the center are equal.
Equal chords of a circle subtend equal angles at the center. If angles subtended by two chords at the center are equal, then the chords are equal.
Of any two chords of a circle the one which is larger is nearer to the center. Of any two chords of a circle the one which is nearer to the center is larger.
 

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