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 Test Yourself - 3 Measurement of angle Types of angle: Right angle Obtuse angle Acute angle Straight angle

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 Ray BA and BC are two non-collinear 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.

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

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 Vertically opposite angles Complimentary angles Supplementary angles Linear pairs of angles

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

Vertically Opposite Angles Vertically opposite 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. Vertically opposite angles are congruent. Point of intersection ‘P’ is the common vertex of the four 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

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

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

Adjacent angles: ÐAPC and ÐCPD Name the vertically opposite angles and adjacent angles in the given figure: A D B C P Vertically opposite angles: ÐAPC and ÐBPD Adjacent angles: ÐAPC and ÐCPD ÐAPB and ÐCPD ÐAPB and ÐBPD

Pairs Of Angles Formed by a Transversal A line that intersects two or more lines at different points is called a transversal. G F Line L (transversal) Line M B A P Line N D C Q Four angles are formed at point P and another four at point Q by the transversal L. Line M and line N are parallel lines. Line L intersects line M and line N at point P and Q. Eight angles are formed in all by the transversal L.

Pairs Of Angles Formed by a Transversal Corresponding angles Alternate angles Interior angles

Corresponding Angles ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. Line M B A Line N D E L P Q G F Line L ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.

Alternate Angles ÐBPQ = ÐDQP ÐAPQ = ÐEQP Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M B A Line N D E L P Q G F Line L ÐBPQ = ÐDQP ÐAPQ = ÐEQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.

Interior Angles ÐBPQ + ÐEQP = 1800 ÐAPQ + ÐDQP = 1800 The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. Line M B A Line N D E L P Q G F Line L ÐBPQ + ÐEQP = 1800 600 1200 600 1200 ÐAPQ + ÐDQP = 1800 The measures of interior angles in each pair add up to 1800. A pair of interior angles lie on the same side of the transversal.

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