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Power Point on what is an angle

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2. 2. Contents • Recap the terms • Angles in daily life • What is an angle? • Naming an angle • Interior and exterior of an angle • Measurement of angle • Types of angle: Right angle Obtuse angle Acute angle Straight angle • Test Yourself - 1 • Congruent angles • Pairs of angles: Types • Test Yourself - 2 • Pairs of angles formed by a transversal • Test Yourself - 3
3. 3. • Imagine • Imagine you lived in a two-dimensional world. You could travel around, visit friends, but nothing in your world would have height. • You could measure distances and angles. • You could travel fast or slow. You could go forward, backwards or sideways. You could move in straight lines, circles, or anything so long as you never go up or down. What is a Plane?
4. 4. Point An exact location on a plane is called a point. Line Line segment Ray A straight path on a plane, extending in both directions with no endpoints, is called a line. A part of a line that has two endpoints and thus has a definite length is called a line segment. A line segment extended indefinitely in one direction is called a ray. Recap Geometrical Terms
5. 5. If we look around us, we will see angles everywhere. Angles In Daily Life
6. 6. Common endpoint B C B A Ray BC Ray BA Ray BA and BC are two non-collinear rays When two non-collinear rays join with a common endpoint (origin) an angle is formed. What Is An Angle ? Common endpoint is called the vertex of the angle. B is the vertex of ∠ABC. Ray BA and ray BC are called the arms of ∠ABC.
7. 7. Fact: We can also think of an angle formed by rotating one ray away from its initial position.
8. 8. To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. For example: ∠ABC or ∠CBA We may also name this angle only by the single letter of the vertex, for example ∠B. A B C Naming An Angle
9. 9. An angle divides the points on the plane into three regions: A B C F R P T X InteriorAnd ExteriorOf An Angle • Points lying on the angle (An angle) • Points within the angle (Its interior portion. ) • Points outside the angle (Its exterior portion. )
10. 10. Angles are accurately measured in degrees. Protractor is used to measure and draw angles. Measurement Of An Angle
11. 11. There are four main types of angles. Straight angle Right angle Acute angle Obtuse angle A B C A B C A B C BA C Types Of Angles
12. 12. Right angle: An angle whose measure is 90 degrees. Right Angle Acute AngleStraight Angle Obtuse Angle
13. 13. Examples Of Right Angle
14. 14. Obtuse angle: An angle whose measure is greater than 90 degrees. Right Angle Acute AngleStraight Angle Obtuse Angle
15. 15. Examples Of Obtuse Angle
16. 16. Acute angle: An angle whose measure is less than 90 degrees. Right Angle Acute AngleStraight Angle Obtuse Angle
17. 17. Examples Of Acute Angle
18. 18. Straight angle: An angle whose measure is 180 degrees. Right Angle Acute AngleStraight Angle Obtuse Angle
19. 19. Examples Of Straight Angle
20. 20. A B C D E F P Q R Which of the angles below is a right angle, less than a right angle and greater than a right angle? Right angle Greater than a right angle Less than a right angle 1. 2. 3.
21. 21. Two angles that have the same measure are called congruent angles. Congruent angles have the same size and shape. A B C 300 D E F 300 D E F 300 Congruent Angles
22. 22. Pairs Of Angles : Types • Adjacent angles • Vertically opposite angles • Complimentary angles • Supplementary angles • Linear pairs of angles
23. 23. 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 Adjacent Angles ∠ABD and ∠DBC Adjacent angles do not overlap each other. D E F A B C ∠ABC and ∠DEF are not adjacent angles
24. 24. Vertically Opposite Angles Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. ∠APC = ∠BPD ∠APB = ∠CPD A DB C P Four angles are formed at the point of intersection. Point of intersection ‘P’ is the common vertex of the four angles. Vertically opposite angles are congruent.
25. 25. If the sum of two angles is 900 , then they are called complimentary angles. 600 A B C 300 D E F ∠ABC and ∠DEF are complimentary because 600 + 300 = 900 ∠ABC + ∠DEF Complimentary Angles
26. 26. 700 D E F 300 p Q R If the sum of two angles is more than 900 or less than 900 , then they not complimentary angles. ∠DEF and ∠PQR are not complimentary because 700 + 300 = 1000 ∠DEF + ∠PQR Contd….
27. 27. If the sum of two angles is 1800 then they are called supplementary angles. ∠PQR and ∠ABC are supplementary, because 1000 + 800 = 1800 RQ P A B C 1000 800 ∠PQR + ∠ABC Supplementary Angles
28. 28. If the sum of two angles is more than 1800 or less than 1800 , then they are not supplementary angles. ∠DEF and ∠PQR are not supplementary because ∠ABC + ∠DEF 1100 + 800 = 1900 D E F 800 CB A 1100 Contd….
29. 29. Two adjacent supplementary angles are called linear pair of angles. A 600 1200 PC D 600 + 1200 = 1800 ∠APC + ∠APD LinearPairOf Angles
30. 30. Name the adjacent angles and linear pair of angles in the given figure: Adjacent angles: ∠ABD and ∠DBC ∠ABE and ∠DBA Linear pair of angles: ∠EBA, ∠ABC C D B A E 600 300 900 ∠EBD, ∠DBC C D B A E 600 300 900
31. 31. Name the vertically opposite angles and adjacent angles in the given figure: A D B C P Vertically opposite angles: ∠APC and ∠BPD ∠APB and ∠CPD Adjacent angles: ∠APC and ∠CPD ∠APB and ∠BPD
32. 32. A line that intersects two or more lines at different points is called a transversal. Line L (transversal) BA Line M Line N DC P Q G F Pairs Of Angles Formed by a Transversal Line M and line N are parallel lines.Line L intersects line M and line N at point P and Q.Four angles are formed at point P and another four at point Q by the transversal L. Eight angles are formed in all by the transversal L.
33. 33. Pairs Of Angles Formed by a Transversal • Corresponding angles • Alternate angles • Interior angles
34. 34. Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent. ∠GPB = ∠PQE ∠GPA = ∠PQD ∠BPQ = ∠EQF ∠APQ = ∠DQF Line M BA Line N D E L P Q G F Line L
35. 35. Alternate Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M BA Line N D E L P Q G F Line L ∠BPQ = ∠DQP ∠APQ = ∠EQP Pairs of alternate angles are congruent. Two pairs of alternate angles are formed.
36. 36. The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. A pair of interior angles lie on the same side of the transversal. The measures of interior angles in each pair add up to 1800 . InteriorAngles Line M BA Line N D E L P Q G F Line L 600 1200 1200 600 ∠BPQ + ∠EQP = 1800 ∠APQ + ∠DQP = 1800
37. 37. Name the pairs of the following angles formed by a transversal. Line M BA Line N D E P Q G F Line L Line M BA Line N D E P Q G F Line L Line M BA Line N D E P Q G F Line L 500 1300