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Polygons
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Triangle Sides = 3 , Vertices = 3 , Angles = 3
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Quadrilateral Sides = 4 , Vertices = 4 , Angles = 4
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Properties of quadrilaterals
All quadrilaterals : have 2 pairs of Equal & Parallel sides Except Trapezoid : has only 1 pair of parallel sides The Square & the Rectangle : have 4 pairs of perpendicular sides (OR) We can say Square & Rectangle : All angles are right (90)
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Pentagon Sides = 5 , Vertices = 5 , Angles = 5
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Hexagon Sides = 6 , Vertices = 6 , Angles = 6
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Heptagon Sides = 7 , Vertices = 7 , Angles = 7
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Octagon Sides = 8 , Vertices = 8 , Angles = 8
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Nonagon Sides = 9 , Vertices = 9 , Angles = 9
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Decagon Sides = 10 , Vertices = 10 , Angles = 10
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Regular & Irregular polygons
All Side lengths are = All Angles are = in measure Irregular Polygons Not all Sides are = in lengths Not all angles are = in measure * * *
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Polyhedrons
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Polyhedrons Polyhedron : Is a 3-D figure in which each side is a flat surface / doesn’t have any curved surfaces Polyhedrons is derived from Poly = many , hedron = face So polyhedron = many faces geometric shape
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Prism Is a polyhedron with 2 congruent bases
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Prisms 1) Triangular Prism Base : Triangle
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Prisms 2) Rectangular Prism = Cuboid Base : Rectangle
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Prisms 2) Pentagonal Prism Base : Pentagon
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Prisms 2) Hexagonal Prism Base : Hexagon
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Prisms 2) Octagonal Prism Base : Octagon
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Pyramids
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Pyramids Is a polyhedron that has 1 base & go to a point at a top
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Pyramids 1) Triangular Pyramid Base : Triangle
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Pyramids 2) Rectangular Pyramid Base : Rectangle
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Pyramids 3) Square Pyramid Base : Square
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Pyramids 4) Pentagonal Pyramid Base : Pentagon
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Non – Polyhedrons Cone Has 1 curved surface – polyhedrons has no curves Has 1 circular base - which is not polygon Sphere Has no bases
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Non – Polyhedrons Cylinder
Has 1 curved surface – polyhedrons has no curves Has 2 circular base - which is not polygon Triangle Is not a 3-D shape
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Volumes Volume of a prism = L x W x H
Where L is the length , W is the width , H is the height
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Volume = L x W x H Volume = 8 x 5 x 10 = 40 x 10 =400 cubic cm
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Volume = L x W x H Volume = 3 x 4 x 6 = 12 x 6 = 72 cubic cm
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According to its measures of angles
Types Of Triangles According to its measures of angles
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Acute Angle Triangle Definition: ACUTE Triangle a triangle in which all angles are acute. Greatest angle : Acute
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Right Angled Triangle Definition: RIGHT Triangle a triangle in which one of the angles is a right angle. Greatest angle : Right Any triangle has at most 1 right angle C B A 60 30
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Obtuse Angle Triangle Definition: OBTUSE Triangle a triangle in which one of the angles is an obtuse angle. Greatest angle : Obtuse Any triangle has at most 1 Obtuse angle
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According to its side lengths
Types Of Triangles According to its side lengths
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Scalene Triangle Definition: Scalene
Triangle: a triangle in which NO sides are equal. 5 cm 3 cm 4 cm
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Isosceles Triangle Definition: Isosceles
Triangle: a triangle in which 2 sides are congruent. 7 cm 7 cm 3 cm
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Equilateral Triangle Definition: Equilateral Triangle: a triangle in which All sides are equal. * * *
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Simplifying Fraction If the Ones are: 0,0 ÷ 10 0,5 ÷ 5 5,5 ÷ 5
0, ÷ 10 0, ÷ 5 5, ÷ 5 Even No ÷ 2 Even , Odd ÷ Odd Sum of digits = No. in table ÷ 3
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Fractions Any proper fraction < 1 ex: 3 4 < 1
Any Improper fraction > ex: > 1 = (3 × 4) = 13 4 20 3 = …. 3 = 6 2 3 3 x 6 = 18 6 3 20 - 18 ---- 2
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Comparing Any No. x proper fraction < Same No. 3 x 3 4 < 3
Any No. x Improper fraction > Same No. x > 3
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