Angles and Lines

Standard of Competence: Understand the relation line and line, line and angle, angle and angle, and how to measure its Basic Competence: 1.Determine the relation of two lines, the kind of angle and its value 2.Understand the property of combined angle if two intersection crossing line or parallel lines intersect with the other line 3.Draw an angle 4.Devide an angle

Non-collinear ray 3 What is an angle? A B C Common endpoint called: VERTEX Non-collinear Ray INTERIOR EXTERIOR A B C The part of angle: 1.Vertex (B) 2.Side/Leg/Arm (BA, BC) 3.Area of angle : interior, exterior The part of angle: 1.Vertex (B) 2.Side/Leg/Arm (BA, BC) 3.Area of angle : interior, exterior Angle is a region forming from two non-collinear rays that has same common endpoint.

Name and Angle Notation  The notation of angle is “ ∠ ” followed by the name of the angle  Name of an angle can be exspresses in 4 ways, that are: 1. Using Greek Letters the Greek letters that usualy used are : α (alpha), β (beta) θ (tetha), γ (gamma) etc the following angle can be written as “ ∠ α” or “angle alpha” 2. Using number (natural numbers) the angle on the right can be written as: “ ∠3” or “angle three” α 3

3. Using three alphabetical letters to named an angle using three letters, the name of its vertex should be placed in the middle. So, the name of angle on the left is ∠PQR or ∠RQP. The letters that used to named an angle should capital letters. 4. Using one alphabetical letter the name of an angle using one letter is same with the name of its vertex. So, the name of angle on the left is ∠L R Q P M L K

How many ways may we call this angle? ABC CBA B 1 A B C 1

Exercises 1. Named of the following angles in 4 different ways. F E D R T P θ 1 (a) (b) 2. How many angles are on the following figure? What are they? R Q S P

Unit of Angles Sexagesimal System 1 o = 60’ 1’ = 60’’ 1 o = 60 x 60’’ = 3,600’’ 1’ = (1/60) o 1’’ = (1/60)’ 1’’ = (1/3,600) o 1 o = 60’ 1’ = 60’’ 1 o = 60 x 60’’ = 3,600’’ 1’ = (1/60) o 1’’ = (1/60)’ 1’’ = (1/3,600) o  1 o read as one degree  60’ read as sixty minutes  60’’ read as sixty seconds The unit of angle we can use: Degree of arc ( o ) Minute of arc ( ’ ) Second of arc ( ’’)

Example 1: 1.4 o =... ’ 2.85’’ =... ’.... ’’ o =... o... ’ 4.(3/4) o =... ’ Solving: Remember! 1 o = 60’ and 1’ = 60’’ 1.4 o = 4 x 60’ = 240’ 2.85’’ = 1’ 25’’ → 85’’ = 60’’ + 25’’ = 1’ + 25’’ o = 40 o 12’ → 0.2 o = 0.2 x 60’ = 12’ 4.(3/4) o = 45’ → (3/4) o = (3/4) x 60’ = 45’

Example: 1.29 o 16’20’’ + 20 o 56’58’’= o 06’35’’ + 29 o 56’57’’=.... Solving: Remember! 1 o = 60’ and 1’ = 60’’ 1.29 o 16’20’’ + 20 o 56’58’’= o 16’ 20’’ 20 o 56’ 58’’ 49 o 72’ 78’’ = 49 o + (1 o + 12’) + (1’ + 18’’) = 50 o 13’18’’

Exercises 1.6’=... ’’ 2.96 ’ =... o.... ’ o =... o... ’ ’ =... ’... ’’ 5.25 o 24’=... O 6.78 o 115’ =... o.... ’ 7.25 o 76’ 88’’ =... o....’....’’ 8.35 o 46’ 28’’ + 45 o 38’ 50’’ =... o....’....’’ 9.43 o 12’ 26’’ + 18 o 38’ 30’’ =... o....’....’’ o 23’ 12’’ – 32 o 48’ 52’’ =... o....’....’’