Types of 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

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

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 For example: ÐABC or ÐCBA We may also name this angle only by the single letter of the vertex, for example ÐB.

Measurement Of An Angle A 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.

Obtuse angle: An angle whose measure is greater than 90 degrees.

Acute angle: An angle whose measure is less than 90 degrees.

Straight angle: An angle whose measure is 180 degrees.

Test Yourself 1 1. D E F 2. P Q R A B C 3. Which of the angles below is a right angle, an obtuse angle, and an acute angle? 1. D E F 2. P Q R Test Yourself 1 Obtuse Angle A B C Right Angle 3. Acute Angle

Pairs Of Angles : Types Adjacent Angles Vertical Angles Congruent Angles Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles Linear Angles

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.

Adjacent Angles ABC and DEF are not adjacent angles 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 ABD and DBC ABC and DEF are not adjacent angles Adjacent angles do not overlap each other.

Vertical Angles ÐAPC = ÐBPD ÐAPB = ÐCPD Vertical angles are pairs of angles formed by two lines intersecting at a point. A D B C ÐAPC = ÐBPD P ÐAPB = ÐCPD Four angles are formed at the point of intersection. Vertical angles are congruent. Point of intersection ‘P’ is the common vertex of the four angles.

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

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

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

ÐABD and ÐDBC Test Yourself 2 ÐABE and ÐDBA ÐEBA, ÐABC ÐEBD, ÐDBC Name a pair of adjacent angles and a 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 angles: ÐEBA, ÐABC ÐEBD, ÐDBC

Adjacent angles: ÐAPC and ÐCPD Name a pair vertical angles and a pair of adjacent angles in the given figure: A D B C P Adjacent angles: ÐAPC and ÐCPD Vertical angles: ÐAPC and ÐBPD ÐAPB and ÐBPD ÐAPB and ÐCPD

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