Polygons

Triangle Sides = 3 , Vertices = 3 , Angles = 3

Quadrilateral Sides = 4 , Vertices = 4 , Angles = 4

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)

Pentagon Sides = 5 , Vertices = 5 , Angles = 5

Hexagon Sides = 6 , Vertices = 6 , Angles = 6

Heptagon Sides = 7 , Vertices = 7 , Angles = 7

Octagon Sides = 8 , Vertices = 8 , Angles = 8

Nonagon Sides = 9 , Vertices = 9 , Angles = 9

Decagon Sides = 10 , Vertices = 10 , Angles = 10

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 * * *

Polyhedrons

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

Prism Is a polyhedron with 2 congruent bases

Prisms 1) Triangular Prism Base : Triangle

Prisms 2) Rectangular Prism = Cuboid Base : Rectangle

Prisms 2) Pentagonal Prism Base : Pentagon

Prisms 2) Hexagonal Prism Base : Hexagon

Prisms 2) Octagonal Prism Base : Octagon

Pyramids

Pyramids Is a polyhedron that has 1 base & go to a point at a top

Pyramids 1) Triangular Pyramid Base : Triangle

Pyramids 2) Rectangular Pyramid Base : Rectangle

Pyramids 3) Square Pyramid Base : Square

Pyramids 4) Pentagonal Pyramid Base : Pentagon

Non – Polyhedrons Cone Has 1 curved surface – polyhedrons has no curves Has 1 circular base - which is not polygon Sphere Has no bases

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

Volumes Volume of a prism = L x W x H Where L is the length , W is the width , H is the height

Volume = L x W x H Volume = 8 x 5 x 10 = 40 x 10 =400 cubic cm

Volume = L x W x H Volume = 3 x 4 x 6 = 12 x 6 = 72 cubic cm

According to its measures of angles Types Of Triangles According to its measures of angles

Acute Angle Triangle Definition: ACUTE Triangle a triangle in which all angles are acute. Greatest angle : Acute

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

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

According to its side lengths Types Of Triangles According to its side lengths

Scalene Triangle Definition: Scalene Triangle: a triangle in which NO sides are equal. 5 cm 3 cm 4 cm

Isosceles Triangle Definition: Isosceles Triangle: a triangle in which 2 sides are congruent. 7 cm 7 cm 3 cm

Equilateral Triangle Definition: Equilateral Triangle: a triangle in which All sides are equal. * * *

Simplifying Fraction If the Ones are: 0,0 ÷ 10 0,5 ÷ 5 5,5 ÷ 5 0,0 ÷ 10 0,5 ÷ 5 5,5 ÷ 5 Even No. ÷ 2 Even , Odd ÷ Odd Sum of digits = No. in table 3 ÷ 3

Fractions Any proper fraction < 1 ex: 3 4 < 1 Any Improper fraction > 1 ex: 4 3 > 1 3 1 4 = (3 × 4) + 1 4 = 13 4 20 3 = …. 3 = 6 2 3 3 x 6 = 18 6 3 20 - 18 ---- 2

Comparing Any No. x proper fraction < Same No. 3 x 3 4 < 3 Any No. x Improper fraction > Same No. 3 x 4 3 > 3