Copyright © Ed2Net Learning, Inc.1 Quadrilaterals Grade 4
Copyright © Ed2Net Learning, Inc.2 Let’s warm up : Angles of the triangle is given. What type of triangles are the following? 1) 53º, 55º and 72º. 2) 110º, 65º and 5º. 3) 26º, 90º and 64º. 4) 45º, 90º and 45º.
Copyright © Ed2Net Learning, Inc. 3 A triangle is one of the basic shapes of geometry: A polygon with three corners or vertices and three sides or edges which are line segments. We learnt about triangles. The three angles always add to 180°. vertex arm B A Cc b a angle ACB Or angle c Let’s review what we did in the last session
Copyright © Ed2Net Learning, Inc. 4 Interior Angle: An Interior Angle is an angle inside a shape. Interior Angle Exterior Angle 45° 135° Exterior Angle: The Exterior Angle is the angle between any side of a shape, and a line extended from the next side. If you add up the Interior Angle and Exterior Angle you get a straight line, 180°. Review
Copyright © Ed2Net Learning, Inc. 5 The basic elements of any triangle are its sides and vertices. Triangles are classified depending on relative sizes of their elements. Triangles can be classified according to their internal angles. Acute Triangle: An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). B A C c b a In the acute triangle shown above, a, b and c are all acute angles. Triangle Classification Review
Copyright © Ed2Net Learning, Inc. 6 Right Triangle: A right triangle is a triangle with a right angle (i.e. 90°). hypotenuse 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. leg b° 90° a° right angle Review
Copyright © Ed2Net Learning, Inc. 7 Obtuse Triangle: An obtuse triangle has one obtuse angle (i.e. greater than 90º). The longest side is always opposite the obtuse angle. In the obtuse triangle shown above, a is the obtuse angle. >90° a° b° Review
Copyright © Ed2Net Learning, Inc. 8 The triangle classification is summarized as follows: There are three special names given to triangles that tell how many sides (or angles) are equal. Equilateral Triangle: An equilateral triangle has all three sides equal in length. Its three angles are also equal and they are each 60º. a aa 60º Types of Triangles Review
Copyright © Ed2Net Learning, Inc. 9 Isosceles Triangle: An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal. aa xº Scalene Triangle: A scalene triangle has no sides of equal length. Its angles are also all different in size. a b c xº yº zº Review
Copyright © Ed2Net Learning, Inc. 10 Combining the Names Right Isosceles Triangle: One right angle. Two equal sides. Two other equal angles always of 45°. Right Scalene Triangle: One right angle. No equal sides. Two other unequal angles. There are two types of right angled triangle: Remember the little square in the triangle tells us that it is a right angled triangle. Review
Copyright © Ed2Net Learning, Inc. 11 Let’s start with Quadrilaterals and other polygons (rectangle, square, rhombus, parallelogram, trapezoid) A polygon is a plane shape with straight sides. Types of Polygons Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself. Simple Polygon Complex Polygon
Copyright © Ed2Net Learning, Inc. 12 Concave or Convex: A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°. If there are any internal angles greater than 180° then it is concave. Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular. convex Polygon concave Polygon regular Polygon irregular Polygon
Copyright © Ed2Net Learning, Inc. 13 Names of Polygons NameSidesShape Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10
Copyright © Ed2Net Learning, Inc. 14 There are many different kinds of quadrilaterals, but all have several things in common: all of them have four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360 degrees. But the sides have to be straight, and it has to be 2-dimensional. We will learn about quadrilateral today. A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on.
Copyright © Ed2Net Learning, Inc. 15 Types of Quadrilaterals There are special types of quadrilateral : the rectangle the rhombus the square the kite those are all parallelograms
Copyright © Ed2Net Learning, Inc. 16 Also opposite sides are parallel and of equal length. The Rhombus: A rhombus is a four-sided shape where all sides have equal length. a c b d The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e. 90°).
Copyright © Ed2Net Learning, Inc. 17 The Square: A Square is a four-sided shape which has all the sides equal and where every angle is a right angle (i.e. 90°). Also opposite sides of a square are parallel. A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).
Copyright © Ed2Net Learning, Inc. 18 The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same). a b a b The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel. NOTE: Squares, Rectangles and Rhombuses are all Parallelograms! A trapezoid is not a parallelogram because only one pair of sides is parallel.
Copyright © Ed2Net Learning, Inc. 19 BREAK
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Copyright © Ed2Net Learning, Inc. 21 Assignments Classify each quadrilaterals as rectangle, square, rhombus, parallelogram, trapezoid: a c b d a b a b 1) 2) 3)
Copyright © Ed2Net Learning, Inc. 22 Classify each quadrilaterals as rectangle, square, rhombus, parallelogram, trapezoid: a b a b 4) 5) 6) 7)
Copyright © Ed2Net Learning, Inc. 23 Write the given figure is a polygon or not a polygon. 8)9) 10)
Copyright © Ed2Net Learning, Inc. 24 A polygon is a plane shape with straight sides. Types of Polygons Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Simple Polygon Complex Polygon Very Good! Let's Review
Copyright © Ed2Net Learning, Inc. 25 Concave or Convex: A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°. If there are any internal angles greater than 180° then it is concave. Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular. convex Polygon Concave Polygon Regular Polygon irregular Polygon
Copyright © Ed2Net Learning, Inc. 26 Names of Polygons NameSidesShape Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10
Copyright © Ed2Net Learning, Inc. 27 There are many different kinds of quadrilaterals, but all have several things in common: all of them have four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360 degrees. But the sides have to be straight, and it has to be 2-dimensional. A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on. Review
Copyright © Ed2Net Learning, Inc. 28 Also opposite sides are parallel and of equal length. The Rhombus: A rhombus is a four-sided shape where all sides have equal length. a c b d The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e. 90°). Review Types of Quadrilaterals
Copyright © Ed2Net Learning, Inc. 29 The Square: A Square is a four-sided shape which has all the sides equal and where every angle is a right angle (i.e. 90°). Also opposite sides of a square are parallel. A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length). Review
Copyright © Ed2Net Learning, Inc. 30 The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same). a b a b The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel. NOTE: Squares, Rectangles and Rhombuses are all Parallelograms! A trapezoid is not a parallelogram because only one pair of sides is parallel. Review
Copyright © Ed2Net Learning, Inc. 31 You have done a nice job. See you in the next session.