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 […]
Read More →Rhombus – Definition – Properties Definition: A rhombus is a quadrilateral (closed shape, plane figure) with four straight sides that are equal length also opposite sides are parallel and opposite angles are equal. A rhombuses is a type of parallelogram. All rhombuses are parallelograms, but not all parallelograms are rhombuses. All squares are rhombuses, but not all […]
Read More →Theorem – The line segment joining the mid-points of two sides of a triangle is parallel to the third side. Given: A triangle △ABC, in which D and E are mid points of sides AB and AC respectively. DE is joined. To prove: Line joining the mid points D and E (DE) is parallel to the third line […]
Read More →Theorem – Alternate Interior Angles are Equal If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. Given: Two parallel Lines AB and CD, and PS be transversal intersecting AB at Q and CD at R. To Prove: Each pair of alternate interior angles are equal. i.e. ∠BQR = ∠CRQ and ∠AQR = ∠QRD […]
Read More →Exterior Angle of a Triangle If any side of a triangle is extended then the exterior angle of triangle is equal to the sum of its interior opposite angles. Given : A △ABC, side BC of △ABC is extended, ∠ACD is an exterior angle. To Prove : The sum of measure of exterior angle of triangle is equal to the sum […]
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 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 →If two Lines are parallel to a third line then the lines are parallel to each other. Given: It is given that three lines l, m, and n, and line l ∥ line m and line m ∥ line n. To Prove: Line l ∥ Line n Proof: Let us draw a line p transversal for lines l, m, and n. For lines l […]
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 →Properties of a Rectangle A rectangle is a two dimensional four sided polygon(quadrilateral), in which the opposite sides are equal and parallel to each other and all four angles are right angles. In figure ABCD is a rectangle. Properties of a Rectangle A rectangle is a quadrilateral. 1. Each interior angle is a right angle. 2. […]
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