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Transcript
A Point A point is used to indicate a location or position. We often use a dot ( ●) to mark a point. ● ● Point A Point B ● Point C Collinear Points ● U L O V collinear points E F N noncollinear points Points that lie on the same line are called collinear points. If there is no line on which all of the points lie, then they are noncollinear points. Lines and Line Segments A line has no endpoints, therefore you A line segment 2 cannot measurehowever, how longhas it is. endpoints and the length of a line segment can be measured. Line AB A A B 8cm B A Ray A ray is part of a line. A ray has one endpoint and go on infinitely in one direction. A ray cannot be measured because it only has one endpoint. B B A Ray AB Ray BA A Curved Lines A B A line can also be curved. A curved line is called a curve. Intersecting Lines or Segments ● Intersecting lines or segments meet at a point. Concurrent Lines or Line Segments ● Concurrent lines or line segments occur when 3 or more lines meet at the same point. Perpendicular Lines or Line Segments Right angle When two lines cut to form right angles (900), we say that the lines are perpendicular. Parallel Lines or Line Segments Two straight lines in a plane are parallel lines if they do not intersect . Skew Lines Line n Line m Skew Lines Line n Line m Skew Lines cannot intersect as they are not on the same plane PLANES Surface of a blackboard Surface of a mirror Cover of a box Surface of a can Examples of plane surfaces A plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. A single capital letter is used to denote a plane. ANGLES Here are some examples of angles. A Sides Vertex B C Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. We find everyday life examples that suggest the idea of an angle. Naming an angle . P● A ● B x ● W ● C Many different names exist for the same angle. For the angle above, ∠PBC,∠ PBW, ∠CBP, ∠WBA and ∠x are all names for the same angle. Measuring Angles The instrument used to measure angles is called a protractor . The unit used is called degree (0) The measurement of an angle is based on a circle divided into 360 parts called degrees(0). A complete turn ( a full circle) is 3600. 900 00, 3600 1800 2700 Classification of Angles 1. Acute Angles An acute angle is an angle less than 90 degrees. 630 250 160 850 80 2. Right Angles A right angle is an angle of exactly 900. 3. Obtuse Angles An obtuse angle is angle greater than 900 but less than 1800. 1500 1250 1100 4. Reflex Angles A reflex angle is an angle greater than 1800 but less than 3600. 2100 PAIRS OF ANGLES Complementary Angles Complementary angles are two angles which add up to 900. The two angles may or may not be adjacent. 400 300 600 500 Supplementary Angles Supplementary angles are two angles whose sum is 1800. The two angles may or may not be adjacent. 1300 500 600 1200 Adjacent Angles Adjacent angles are two angles lying next to each other on the same plane with a common vertex and a common side between them. C P Q 1300 300 A M B 500 D 600 R S A H T Vertical angles When two lines intersect each other, the angles “opposite “ each other are known as vertically opposite angles. S b P c a d Q R Vertically opposite angles are equal. ∠a = ∠ c ∠b = ∠d Salamat sa inyong lahat Prepared by: Mrs. Flordelita G. Male Master Teacher II San Bartolome High School Quezon City