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Section 1.4 Measuring Segments and Angles Goal: After today, you will be able to: Explain the Ruler Postulate and the Segment Addition Postulate. Use the Ruler Postulate and the Segment Addition Postulate find the lengths of segments. Use the midpoint and some algebra skills to find the lengths of segments. Coordinates Definition: A coordinate is a point’s distance and direction from zero on a number line. Note the Notation for “length” 3 Postulates Postulate 1-5 The Ruler Postulate: The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. | | PK = 3 - -2 = 5 (distance is always positive) Congruent Segments Congruent segments are Definition: segments with the same length. Congruent segments can be marked with . . . REMEMBER THIS POINT: Numbers are equal to each other. Shapes and figures are not equal to each other. But if their MEASURES are equal, then they are congruent. Correct notation: Incorrect notation: Segment versus length - notation 6 Midpoint Definition: a point that divides a segment into two congruent segments We also say that E bisects the segment. “Between” Definition: X is between A and B if AX + XB = AB. AX + XB = AB So, X is between Points A and B AX + XB > AB Since not = ; we can conclude That X is NOT ‘between’ points A and B Segment Addition Postulate! (is something you already know how to use) home school movies Philly The Segment Addition Postulate: If three points A, B, and C are collinear and C is between A and B, then: AC + CB = AB Example: If AC = x , CB = 2x and AB = 12, then Find x, AC and CB. AC + CB = AC x + 2x = 12 3x = 12 x=4 Final Answer: x = 4 AC = 4 CB = 8 2x x 12 Classwork Time. Page 29-30 #’s 1-15 Odd. Read pages 27-29 Try #’s 18, 20-23, 27 11 Section 1.4b - Angles 12 Measuring Angles Goals: 1. Define terms used in relation to angles. 2. Name angles in several ways. 3. Measure and classify angles. 4. Identify congruent angles. 5. Recognize special pairs of angles. 13 Angle Terms - An angle is formed by two rays with a common endpoint. - The rays are called the sides. - The common endpoint where the sides meet is called the vertex. - The angle measure is measured in “degrees”. Ex: 55º 14 Naming Angles A 1 C B Or Geek Letters! - Theta - Alpha - Beta Measuring Angles 16 Classifying Angles An acute angle has a measure that is greater than 0 degrees but less than 90 degrees. A right angle has a measure of exactly 90 degrees. An obtuse angle has a measure greater than 90 degrees but less than 180 degrees. A straight angle has a measure of exactly 180 degrees. Congruent angles are angles that have the same measure. 17 Measure and Classify C A m<ABC = B Classify <ABC: 18 Measure and Classify A C m<ABC = B Classify <ABC: 19 Measure and Classify Measure / Classify = = 20 21 Postulate 1-8: The Angle Addition Postulate 22 Using the Angle Addition Postulate 23 Special Pairs of Angles two angles whose sides are opposite rays Vertical Angles are Congruent!! two coplanar angles with a common side, a common vertex, and no common interior points (they don’t overlap) 24 Special Pairs of Angles two angles whose measures have a sum of 90 degrees. two angles whose measure have a sum of 180 degrees. Each angle is called the complement of the other. Each angle is called the supplement of the other. 25 Classwork Page 30, #16, 18, 20-23, 27, 29-32, 42-49 26