Theorem The perpendicular from the center of a circle to a chord bisects the chord. Given: A circle with center O, AB is chord of a circle and OC perpendicular from the center to the chord AB. i.e. OC ⊥ AB therefore ∠OCA and ∠OCB Both angles are 900. To prove: AC = CB (C is the mid point of chord AB) […]
Read More →Area of a Triangle In this lesson we will learn, how to calculate the area of a triangles with different formula’s. When given 1. The base and height of a triangle.2. Two sides and one angle.3. The length of three sides.4. An equilateral triangle. First we see about a triangle. A triangle is a simple […]
Read More →Trigonometric Ratios of Some Specific Angles Trigonometric Ratios Here are Trigonometric Ratios of some Specific angles, 00, 300, 450 , 600 and 900. Example: (1) Find the value of sin600 cos300 + sin300 cos600 Values of Trigonometric Ratios from above table, sin 600 = √3/2, […]
Read More →Elements of a Parallelogram In figure a Parallelogram ABCD. There are four sides AB, BC, CD and DA and four angles ∠A, ∠B, ∠C and ∠D in a Parallelogram. AB and DC are opposite sides, and AD and BC are another pair of opposite sides. ∠A and ∠C are a pair of opposite angles, and another pair of opposite angles are ∠B and ∠D. AB […]
Read More →Parallel Intersecting and Perpendicular Lines Definition: Parallel Lines Two or more lines in a plane that never intersect or touch each other are called “Parallel lines”. The symbol “∥” is used to denote parallel lines. Example- PQ ∥ RS denoted that line PQ parallel to line RS. Intersecting lines […]
Read More →If the angles subtended by chords of a circle at the center are equal, then the chords are equal. Given: A circle with center O, AB and CD are chords of circle that subtend equal angles at center O. i,e. ∠AOB = ∠COD. To prove: chord AB = chord CD Proof: In △AOB and △ CODOA = OC (Radius of circle)∠AOB […]
Read More →Equal chords of a circle subtend equal angles at the center. Given: Two equal chords AB and CD of a circle with center O. i,e. AB = CD. To prove: ∠AOB = ∠COD Proof: In △AOB and △ COD OA = OC (Radius of circle)OB = OD (Radius of circle)AB = CD (Given) Hence, △AOB ≅ △ COD (SSS Congruence rule) ∴ ∠AOB […]
Read More →Angles opposite to equal sides of an isosceles triangle are equal. Given: A isosceles triangle △ ABC in which AB = AC, andangles opposite to equal sides of triangle are ∠B and ∠C. To prove: We need to prove that ∠B and ∠C, are equal ∠B = ∠C. Construction: Draw the bisector […]
Read More →The side opposite to equal angles of a triangle are equal. Given: A triangle △ ABC in which angles opposite to sides AC and AB of are ∠B and ∠C, and ∠B = ∠C. To prove: We need to prove that sides AB and AC, are equal AB = AC. Construction: Draw […]
Read More →Supplementary and Complementary Angels To understand supplementary and complementary angles, first we need to understand the adjacent angles. Adjacent angle Two angles that have a common vertex and a common side but not overlap, are known as adjacent angles. Complementary Angles When the total of […]
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