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Triangles & Quadrilaterals

Triangles & Quadrilaterals. Grade 6. Warm up. State True/ False. The shape with three or more sides is a polygon Hexagon has the maximum number of sides. There are 20 diagonals in a Decagon. Fill in the blanks: ________ is not an irregular polygon

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Triangles & Quadrilaterals

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  1. Triangles & Quadrilaterals Grade 6 Confidential

  2. Warm up State True/ False • The shape with three or more sides is a polygon • Hexagon has the maximum number of sides. • There are 20 diagonals in a Decagon. • Fill in the blanks: • ________ is not an irregular polygon • Nonagon has________ sides. Confidential

  3. Lets review what we have learned Polygons: A polygon is a closed plane figure made up of 3 or more line segments Types of Polygons: Concave, Convex, Regular and Irregular Names of Polygon according to the sides are Triangles, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon and Decagon Confidential

  4. Formulae Sum of Interior Angles= 180(n-2), n denotes the number of sides Each interior angle of a regular polygon = 180(n-2) where n represents number of sides. n Each exterior angle (regular polygon) = 360 , where n represents number of sides. n Confidential

  5. A side 3 side 1 B side 2 C Lets get started Triangle:- A three-sided polygon is called to be a triangle. The sum of all angles in a triangle is 180 degrees. Angle A + Angle B + Angle C = 180 degrees Triangles can be classified according to the length of their sides and the size of their angles. Confidential

  6. Scalene Triangles Equilateral Triangles IsoscelesTriangles Classifying Triangles according to the Length of their Sides Confidential

  7. D x a b E F y z c Scalene Triangles In  DEF, the sides are a, b and c. Angles are x , y and z. A scalene trianglehas no equal sides.Its angles are also all different in size. Confidential

  8. Equilateral Triangles An equilateral triangle has all three sides equal in length. Its three angles are also equal and they are each 60 degrees. Confidential

  9. Isosceles Triangles a a x x An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal. Confidential

  10. Acute-angled Triangles Obtuse-angled Triangles Right-angled Triangles Classifying Triangles according to the Length of their Angles Confidential

  11. b a c Acute-angled Triangle An acute angle is an angle whose measure is greater than 0° and less than 90º. An acute triangle is a triangle whose angles are all acute . In the acute triangle shown below, a,b and c are all acute angles. Confidential

  12. Obtuse-angled Triangle An obtuse angle is an angle whose measure is greater than 90º and less than 180º. An obtuse triangle has one obtuse angle.The longest side called the hypotenuse is always opposite the obtuse angle. a Longest side Confidential

  13. hypotenuse legs 90 legs Right-angled Triangle A right-angled triangle has one angle equal to 90°. That is, one angle is a right angle . The side opposite the right angle is always the triangle's longest side. It is called the hypotenuse of the triangle. The other two sides are called the legs. Confidential

  14. 1) Isosceles triangle Example Name the following triangles: 2) Draw a square around the right triangle: Confidential

  15. Your turn Identify the following types of triangles: 1) ____ - a triangle with no equal sides. 2) ____ - a triangle with a right angle. 3) ____ - a triangle with at least two sides equal. 4) ____ - a triangle with three acute angles. 5) ____ - a triangle with three equal sides. Confidential

  16. Quadrilateral A four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees. The figure represents the types of quadrilaterals. Confidential

  17. Quadrilaterals Family TRAPEZOID Trapezoid is a quadrilateral with only one pair of parallel sides. In regular trapezoid, base angles are equal. Opposite side Base Angle Base Confidential

  18. D C ● ▪ ● ▪ A B PARALLELOGRAM • Opposite sides of a parallelogram are parallel and equal in length. • Opposite angles are equal in size. • Diagonals (AC & BD) bisect each other. • Diagonals form 2 congruent triangles In Parallelogram ABCD, the sides AB and CD are equal. ▪, ● denotes the equal angles. Note: Rectangles and squares are special kinds of parallelograms. Confidential

  19. RHOMBUS • All sides of a rhombus are equal in length • Opposite sides are parallel. • Opposite angles of a rhombus are equal. • The diagonals of a rhombus bisect each other at right angles. AB , CD & AD, BC are parallel. Angle B = Angle D Angle A= Angle C Note: A parallelogram with four equal sides is called a rhombus. Confidential

  20. RECTANGLE • Opposite sides of a rectangle are parallel and equal in length. • All angles are equal to 90°. D C A B Confidential

  21. C D B A SQUARE • Opposite sides of a square are parallel and all sides are equal in length. • All angles are equal to 90°. Confidential

  22. Example • A rectangle has ____ pairs of parallel sides. • In a parallelogram any two opposite angles are _____. • 3) The sum of the angles of a quadrilateral is _____ degrees. • 4) In ________ trapezoid, base angles are equal. • 5) Name the quadrilateral whose angles are 90 degree. Confidential

  23. BREAK TIME!!!! Confidential

  24. Your Turn 1. One of these is not a quadrilateral. (trapezoid, square, triangle, rectangle) 2. Write True or False. Rectangles and Squares are special kinds of Parallelograms. 3. A quadrilateral with only 1 pair of parallel sides is called ________. 4. What is a parallelogram with 4 right angles and 2 pairs of equal sides. 5. Example of quadrilateral is ______. (Rhombus, triangle) Confidential

  25. 80 48 1) Calculate the size of the missing angle in the following triangle. Confidential

  26. D C 68 x B 126 106 A 2) Find the angle x in the given diagram. Confidential

  27. 3) The opposite sides of a parallelogram are represented by 2x+10 and 5x-20.Find the length of the side of the parallelogram represented by 4x-1. Confidential

  28. Lets review what we have learned in our lesson Triangle:Three sided polygon. Types of Triangles:Triangles can be classified according to the length of their sides and the size of their angles. • Scalene Triangle • Isosceles Triangle • Equilateral Triangle • Acute-angled Triangle • Obtuse-angled Triangle • Right-angled Triangle Confidential

  29. Quadrilateral: Four sided polygon. • Types of Quadrilateral: • Trapezoid - a quadrilateral with two parallel sides. • Rhombus - A quadrilateral with four equal sides and opposite angles equal. • Parallelogram - Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other. • Rectangle - A parallelogram in which all angles are right angles. • Square – It is a special case of a rectangle as it has four right angles and parallel sides. Confidential

  30. Sum of angles in a triangle = 180 degrees Sum of angles in a Quadrilateral = 360 degrees Confidential

  31. You did great Today ! Be sure to practice and keep up the good work Confidential

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