Geometry Chapter 1 Section 1-4 Measuring Angles

Recap Geometrical Terms An exact location on a plane is called a point. Point A straight path on a plane, extending in both directions with no endpoints, is called a line. Line A part of a line that has two endpoints and thus has a definite length is called a line segment. Line segment A line segment extended indefinitely in one direction is called a ray. Ray

Ray BA and BC are two non-collinear rays What Is An Angle ? When two non-collinear rays join with a common endpoint (origin) an angle is formed. A Ray BA B Common endpoint B C Ray BC Common endpoint is called the vertex of the angle. B is the vertex of ÐABC. Ray BA and BC are two non-collinear rays Ray BA and ray BC are called the sides of ÐABC.

If we look around us, we will see angles everywhere. Angles In Daily Life If we look around us, we will see angles everywhere.

Naming An Angle A B C For example: ÐABC or ÐCBA To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. A B C 1 For example: ÐABC or ÐCBA We may also name this angle only by the single letter of the vertex, for example ÐB or by a number.

Interior And Exterior Of An Angle An angle divides the points on the plane into three regions: Points lying on the angle (An angle) A B C P T X F R Points within the angle (Its interior portion. ) Points outside the angle (Its exterior portion. )

Measurement Of An Angle One way to measure and angle is in degrees. To indicate the size or degree of an angle write a lower case m in front of the angle symbol. The measure of angle B is 65 degrees You show this by writing m<B = 65. A B C

Measurement Of An Angle Protractor is used to measure and draw angles. Angles are accurately measured in degrees.

There are four main types of angles. Right angle Acute angle Obtuse angle A B C A B C A B C Straight angle B A C

Right angle: An angle whose measure is 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

Examples Of Right Angle

Obtuse angle: An angle whose measure is greater than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

Examples Of Obtuse Angle

Acute angle: An angle whose measure is less than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

Examples Of Acute Angle

Straight angle: An angle whose measure is 180 degrees. Right Angle Acute Angle Obtuse Angle

Examples Of Straight Angle

Greater than a right angle Which of the angles below is a right angle, less than a right angle and greater than a right angle? 1. D E F 2. P Q R Test Yourself 1 Greater than a right angle A B C Right angle 3. Less than a right angle

Congruent Angles A B C D E F D E F Two angles that have the same measure are called congruent angles. A B C 300 D E F 300 D E F 300 Congruent angles have the same size and shape.

Pairs Of Angles : Types Adjacent angles Linear pairs of angles Vertical Angles Complimentary angles Supplementary angles

Adjacent angles do not overlap each other. Two angles that have a common vertex and a common ray are called adjacent angles. C D B A Common ray Common vertex D E F A B C Adjacent Angles ÐABD and ÐDBC ÐABC and ÐDEF are not adjacent angles Adjacent angles do not overlap each other.

Two adjacent supplementary angles are called linear pair of angles. 1200 600 C D P ÐAPC + ÐAPD 600 + 1200 = 1800

Vertical Angle Pairs 1 2 4 3 ∠1 and ∠3 ∠4 and ∠2 Vertical Angles: two angles whose sides are opposite rays. 1 2 4 3 Name the pairs of vertical angles. ∠1 and ∠3 ∠4 and ∠2

Pairs Of Angles : Types Complimentary angles Supplementary angles

ÐABC and ÐDEF are complimentary because Complimentary Angles If the sum of two angles is 900, then they are called complimentary angles. 600 A B C 300 D E F ÐABC and ÐDEF are complimentary because ÐABC + ÐDEF 600 + 300 = 900

ÐDEF and ÐPQR are not complimentary because Contd…. If the sum of two angles is more than 900 or less than 900, then they not complimentary angles. 700 D E F 300 p Q R ÐDEF and ÐPQR are not complimentary because ÐDEF + ÐPQR 700 + 300 = 1000

ÐPQR and ÐABC are supplementary, because Supplementary Angles If the sum of two angles is 1800 then they are called supplementary angles. R Q P A B C 1000 800 ÐPQR and ÐABC are supplementary, because ÐPQR + ÐABC 1000 + 800 = 1800

ÐDEF and ÐPQR are not supplementary because Contd…. If the sum of two angles is more than 1800 or less than 1800, then they are not supplementary angles. C B A 1100 D E F 800 ÐDEF and ÐPQR are not supplementary because ÐABC + ÐDEF 1100 + 800 = 1900

Test Yourself 2 ÐABD and ÐDBC ÐABE and ÐDBA ÐEBA, ÐABC ÐEBD, ÐDBC Name the adjacent angles and linear pair of angles in the given figure: Adjacent angles: C D B A E 600 300 900 C D B A E 600 300 900 ÐABD and ÐDBC ÐABE and ÐDBA Test Yourself 2 Linear pair of angles: ÐEBA, ÐABC ÐEBD, ÐDBC

Pairs Of Angles Your Turn Complete problems on Page 72-73 #18 -25

Modified by Mrs. D. Joseph Excerpts The Department of Research The End Modified by Mrs. D. Joseph Excerpts The Department of Research Bombay Cambridge Gurukul

Contents Recap the terms Test Yourself - 1 Angles in daily life Congruent angles Pairs of angles: Types What is an angle? Test Yourself - 2 Naming an angle Pairs of angles formed by a transversal Interior and exterior of an angle Measurement of angle Test Yourself - 3 Types of angle: Right angle Obtuse angle Acute angle Straight angle