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 →The line drawn through the center of a circle to bisect a chord is perpendicular to the chord. Given: A circle with center O, AB is chord of a circle and OC bisect chord at C. i,e. AC = CB. To prove: OC ⊥ AB Construction: join OA and OB. Proof: In △ OCA and △ OCB OA = OB (Radius […]
Read More →Parallelograms on the same base and between the same parallels are equal in area. Given: Two parallelograms ABCD and EFCD, are on the same base DC and between the same parallel lines AF and DC. To prove: area (∥gm ABCD) = area (∥gm EFCD) Proof: In △ AED and △ BFC BC ∥ AD and AF is a transversal.So, ∠DAE = ∠CBF …..(1) (Corresponding angles of […]
Read More →If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Given: ABCD is a quadrilateral, each pair of opposite sides of quadrilateral ABCD are AB and CD and also sides AD and BC are equal. AB = CD BC = AD To prove: ABCD is a parallelogram. Construction: Join A to C that is AC, is […]
Read More →In a parallelogram opposite sides are equal. Given: A parallelogram ABCD, each pair of Opposite sides of parallelogram are side AB and side DC and side AD and side BC. To prove: Opposite sides of parallelogram are equal that is AB = DC and AD = BC Construction: Join A to C that is AC, is a diagonal, the diagonal AC […]
Read More →Quadrilateral – Definition – Properties There are kinds of quadrilaterals, based on the sides and angles. 1. Parallelogram 2 Rectangle 3. Square 4. Rhombus 5. Trapezium 6. kite 1. Parallelogram A Parallelogram is a quadrilateral, whose both pairs of opposite sides are parallel and equal in length. In above […]
Read More →Square – Properties – Formula Here we will learn, about some geometrical properties of a square. In below figure ABCD is a square. Properties of a square 1. All four sides of a square are equal or congruent. 1. All four sides of a square are equal or congruent. AB = BC = CD = DA 2. All […]
Read More →Common Geometry Symbols Geometry Symbol Symbol Symbol Name (1) ∠ Angle (2) ∟ Right angle (3) ∡ […]
Read More →Vertical Angles When two lines are intersect they made four angles, angles are opposite to one another at the intersection of two lines. Each opposite pair of angles are called “Vertical Angles”, and vertical angles are always “Congruent” They are also called “Vertically Opposite Angles”. In above […]
Read More →If the diagonals of a Quadrilateral, bisect each other then that Quadrilateral is a Parallelogram Given: ABCD is a quadrilateral with AC and BD are diagonals and diagonals intersect each other at O. i.e. OA = OC and OB = OD To Prove: ABCD is a parallelogram. Proof: In △AOD and △COB […]
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