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Transcript

Chapter 1-4 Angles and Segments To Use and apply the Segment Addition Postulate and Angle Addition Postulate To classify angles 1.4 Congruent Segments and Congruent Angles If 2 segments are ≅, they are = in length. If 2 angles are ≅, they are equal in size. Measuring & comparing segments -9 -7 -2 0 2 3 6 9 A B C D E F G H Compare 1. AB ___ EF 3. CD ___DE 2. BC____EG A B C Segment Addition Postulate AB + BC = AC i.e. the parts = the whole M A N 1. If MA = 12 and AN = 11, then MN =______ 2. If MN = 38 and AN = 22, then MA = ______ AC = 38 Find x, AB,& BC. B A 2X + 5 C 3X - 2 N M O -12 MN = 8 MO=21 Find the coordinates of N and O. NO = _____ Midpoint of a segment A point that divides a segment into 2 congruent parts. Segment Bisector A line, line segment, ray or plane that intersects a segment at its midpoint How many midpoints can a segment have? How many segment bisectors can a segment have? A M There are an infinite number of segment bisectors. B 5a - 16 2a + 5 H O Find a, HO, and OT. T M -26 R P -2 If R is the midpt of MP find MR=_____ RP=_____ and the coordinate of R. R -10 4x M 3x P 18 Find x and AB, BC and AC. What are the coordinates of B if C’s coordinate is 70? 6X - 8 A 2X + 20 B C W X Y Z T R -14 -8 -2 0 4 9 Find the possible coordinates of M if YM = 5. Find the possible coordinates of E on YR if YE = 9 Assignments 1st Part of section1.4 Assign pp. 29-31 (1-15 all, 29-35 all) Part II Angles What is an angle? How do you name the following angle? A Angle - the union of 2 noncollinear rays whose intersection is a point called the vertex. <ABC or <CBA or <B B C When naming an angle remember……. The vertex point must always be in the middle A point from each ray should be on either side of the vertex point You can name an angle with the vertex pt if it is the only angle at the vertex Given < ABC Vertex is B Ray BA Ray BC Can be named <CBA or <B Classify Angles Acute angles- angles less than 90 degrees Right angles- angles whose measure = 90 degrees Obtuse angles- angles greater than 90 degrees Straight angles- angles = 180 degrees (a straight line) Draw an example of each type of angle. 1. 2. 3. 4. Complementary Angles 2 angles whose sum is 90 H 1 2 O W Supplementary Angles Two angles whose sum is 180. B H 60 120 E Y T A Adjacent Angles Two angles that have a common ray, a common vertex, and no common interior points. H 1 E P 2 L Linear Pair Two angles that are adjacent and supplementary. D 1 A 2 B C Angle Addition Postulate m < 1 + m < 2 = m <TAP T E 1 A 2 P Find x and the measure of the 2 angles. Definition of Linear Pair 2x + 8 6 x - 84 Find x and each angle. Explain your answer. 4x 2x + 18 Definition of complementary angles. 1 A 2 E 3 D m<1=m<3 m < 1 = 10 less than twice m<2 Find x and the measure of each angle. m < AOB = 4x + 3, m < BOC = 7X, m < AOD = 16X -1 Solve for x and find the angle measures. Assignments 2nd part of 1.4 Pgs 30-33 (16-19,27-28,70-72,75-78) Notebook Quiz 1. Write an equation for the following. 2x + 8 6 x - 84 2. Write an equation for the following: R -10 4x M 3x P 18 Draw a picture to demonstrate each of the following: 3. Complementary Angles 4. Linear Pair Notebook Quiz 1. Write an equation for the following. 2x + 8 6 x - 84 2. Write an equation for the following: R -10 4x M 3x P 18 Draw a picture to demonstrate each of the following: 3. Complementary Angles 4. Linear Pair