PlosMathLearning

Geometry

 

Geometry is the study of size, shape and position of 2 dimensional shapes and 3 dimensional figures.

Basic Terms
  • Lines
  • Line Segments
  • Rays
  • Intersecting Lines
  • Parallel Lines
  • Perpendicular Lines


Lines

  A line extends forever in both directions. A line has no end points. Therefore, we cannot measure how long it is.

 

Line Segments

  A line segment does not extend forever, but has two distinct endpoints. A line segment is a portion of a line.



Rays

  A ray is a straight line that begins at a certain point and extends forever in one direction. Below are two rays going in opposite direction.




Intersecting Lines

  The term intersect is considered when lines, rays, line segments or figures meet, this means, they share a common point.

Parallel Lines

  Two lines in the same plane which never intersect are called parallel lines.

Perpendicular Lines

  Two lines are perpendicular if they intersect at a 90 degree angle.




Types of Angles

 

When two rays share the same endpoint they form an angle. The point where the rays intersect is called the vertex of the angle.

  • Acute Angle
    An acute angle measures more than 0o but less than 90o.

     
  • Right Angle
    A right angle measures exatly 90o.

     
  • Obtuse Angle
    An obture angle measures more than 90o but less than 180o.

     
  • Straight Line Angle
    A straight line angle measures exactly 180o.

     
  • Reflex Angle
    A reflex angle measures more than 180o but less than 360o.

     
  • Complementary Angles
    Two angles are complementary angles if the sum of their angles equals exactly 90 degrees.
     
  • Supplementary Angles
    Two angles are supplementary if the sum of their angles equals exactly 180 degrees.




Types of Triangles

 

A triangle is one of the basic shapes in geometry. A triangle has 3 sides and 3 interior angles. The sum of interior angles is 180o.

The Basic Types of triangles
  • Right-Angled Triangle
    A right-angled triangle has one of its angles measures 90o.
     
  • Scalene triangle
    A scalene triangle has no sides and no angles equal.

     
  • Isosceles Triangle
    An Isosceles triangle has two of is sides and two of it angles equal.
     
  • Equilateral Triangles
    An equilateral triangle has all sides and all angles equal. Each angle in an equilateral triangle measures 60 degrees.
     
  • An Acute Triangle
    An acute triangle has all its angles acute (measures less than 90 degrees).
     
  • Obtuse Triangles
    An obtuse triangle has one of its angle obtuse (measures more than 90 degrees).


Types of Quadrilaterals

  A quadrilateral is a polygon with four sides and four interior angles. The sum of interior angles is 360o

Angle Properties of a Polygon


A regular polygon has all sides equal and all angles equal.

Name of polygonNumber of sidesSum of interior angles
Triangle31800
Quadrilateral43600
Pentagon55400
Hexagon67200
Heptagon79000
Octagon810800
Nonagon912600
Decagon1014400


1. The sum of the interior angles of a regular polygon with "n" number of sides is given by
the formula: sum of interior = 180(n - 2)0.

2. The sum of the exterior angle is 3600.

3. The sum of the interior and exterior angles at any vertex (corner) of a polygon is 1800.

Sample Problems
1. A regular polygon has 7 sides. Calculate the sum of the interior angles.

Solution: Sum of interior
= 180(n - 2)0
= 180(7 - 2)0
= 180(5)0
= 9000

2. A regular polygon has 5 sides. Calculate the size of each interior angle.

Sum of interior angles
= 180(n - 2)0
= 180(5 - 2)0
= 180(3)0
= 5400
Each interior angle = 5400 ÷ 5 = 1080

Another way to solve this problem
Since the sum of the exterior angles of a regular polygon is 3600, the size of each exterior
angle of this polygon with 5 sides would be 3600 ÷ 5.
3600 ÷ 5 = 720.
Also, we know that
exterior angle + interior angle = 1800
720 + interior angle = 1800
Each interior angle = 1800 - 720.
Each interior angle = 1080.






Copyright © 2012 Peter Smith

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