What is an Angle Angles are formed by two rays or lines called the arms or sides of the angle, sharing a common endpoint, called the vertex of the angle. Types of angles There are various types of angles. The angles can be classified into two main types. Basis on their measure or magnitude. Based […]

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 Parallelograms – Properties   A parallelogram is a special type of a polygon. it is a quadrilateral with both pair of opposite sides are parallel. Properties 1. Opposite sides are equal.       Opposite sides, AB = CD and AC = BD 2. Opposite angles are equal.      Opposite angles are ∠A = ∠D and ∠B […]

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Given: Two triangles △ ABC and △ ABD are on same base (or equal bases) AB, and area of △ ABC and △ ABD are equal. Proof: CD ∥ AB Construction: Draw CE and DF perpendicular to AB.So DF is the height of △ ADB, and CE is the height of △ABC. CE perpendicular to AB and DF perpendicular to AB.Since, lines perpendicular to same line […]

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Two triangles on the same base (or equal bases) and between the same parallels are equal in area. Given: △ ABC and △ PBC are two triangles on same base (or equal bases) BC and between the same parallels, BC and AP. To prove: ar △ ABC = ar △ PBC Construction: Through B, draw BD ∥ CA intersecting PA produced at D, and […]

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The sum of the angles of a triangle is 180º Given: A triangle △ PQR and ∠1, ∠2, and ∠3 are angles of triangle △ PQR.  To prove:  ∠1 + ∠2 + ∠3 = 1800 Construction: Draw a line XPY parallel to QR passing through P.  Proof: XPY ∥ QR and PQ is transversal ∴ ∠2 = ∠4 (Alternate angles) ….(1) XPY ∥ QR and PR […]

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  Acute Angle When two rays are joined together at a common point, an angle is formed. Definition: Acute angle: A angle whose measure is more than 0 degree and less than 90 degree is called a acute angle. ∠AOB is a acute angle, it’s measure 45º, which is less then 90 degree and more then […]

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Angle – Definition – Geometry Definition: In plane geometry, angles are formed by two rays or lines called the arms or sides of the angle, sharing a common endpoint, called the vertex of the angle. Angle Symbol An angle is represented by symbol ∠ Angles are measured in degree, which is unit of angle using […]

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 Congruent Figures In our daily life we see many congruent objects like as,  (i) Two 2 Rupees, 5 Rupees, or 10 Rupees coins. (ii) Two text books of mathematics of same class.  Two figures or objects are called congruent, when one object cover the other completely and exactly. This means that two books or coins […]

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