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# Angles

## by khaloi on Mar 08, 2009

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## AnglesPresentation Transcript

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• ANGLES
• An angle ( ) is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle).
• PARTS OF AN ANGLE
• Vertex: A
• B Sides: AB and AC
• exterior of the angle
• interior of
• the angle
• A 1 C
• HOW TO NAME AN ANGLE
• - BAC - CA B - 1 - A
• Angles are measured in degrees.
• The measure of A is written as m A. m A = 45 o .
• CLASSIFICATION OF ANGLES (according to measure)
• x o
• ACUTE x o x o
• 0 < x < 90 o RIGHT
• x = 90 o
• REFLEX
• x o 180 o < x < 360 o x o
• OBTUSE STRAIGHT
• 90 o < x < 180 o x = 180 o
• PROTRACTOR POSTULATE
• Let OA and OB be opposite rays in a plane. OA, OB and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers from 0 o to 180 o in such a way that OA is paired with 0 o to and OB is paired with 180 o or the way around.
• Try This Measure the angles (#s 1 & 2 of Exercise 4-2 C – pg 56)
• Use a protractor to draw a 105 o angle .
• Angles with the same measure are congruent.
• If point B is in the interior of AOC, then
• m AOB + m BOC = m AOC .
• If AOC is a straight angle, then
• m AOB + m BOC = 180 o .
pls. refer to the examples in page 55
• Angle Pairs
• Two coplanar angles are adjacent if and only if they satisfy three conditions:
• they have a common vertex,
• they have common side, and
• they have no common interior points.
• AOB and BOC are adjacent.
• AOB and AOC are not.
• Two angles are complementary if and only if the sum of their measures is equal to 90 o . Each angle is the complement of the other.
• Two angles are supplementary if and only if the sum of their measures is equal to 180 o . Each angle is the supplement of the other
• Two angles are called vertical angles if and if only they are two nonadjacent angles formed by two intersecting lines.
2 1 B A 50 O 40 O 3 4 155 O 25 O A B 1 2 3 4
• VERTICAL ANGLES:
• 1 and 3
• 2 and 4
pls. refer to the examples in page 58
• VERTICAL ANGLE TEST
• If two angles are vertical, then they are congruent.
1 2 3 4