Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MEASURING AND CONSTUCTING SEGMENTS GEOMETRY (HOLT 1-2) K. SANTOS COORDINATE A point corresponds to one and only one number on a ruler. This number is called a coordinate. A 1 2 A has coordinate 1 3 RULER POSTULATE 1-2-1 β’ The points of a line can be put into one-to-one correspondence with the real numbers. A a Where a and b are numbers B b DISTANCE & LENGTH Distance between any two points is the absolute value of the difference of the coordinates. A B a b AB = |a - b|or |b - a| The distance between A and B is also called the length of π΄π΅ FINDING THE LENGTH OF A SEGMENT Find AD, and DF. A B C D E F G H I -5 -4 -3 -2 -1 0 1 2 3 AD = β5 β (β2) AD = β5 + 2 AD = β3 AD = 3 Remember all lengths are positive DF = β2 β 0 DF = β2 DF = 2 DISTANCE BETWEEN POINTS If G is at -12 and H is at 82, find the distance between the points. β12 β (82) β94 94 So, the distance between G and H is 94 units. What is the length of GH? GH = 94 length and distance have the same value CONGRUENT SEGMENTS β’ Two segments with the same length β’ Symbol is β β’ Pictures are marked with βtickβ marks (same number of marks on each congruent piece) B C D A If AB = CD then π΄π΅ β πΆπ· Which is read: If the measure of AB equals the measure of CD then AB is congruent to CD EXAMPLE--CONGRUENT SEGMENTS Find which two of the segments ππ, ππ, and ππare congruent. X Y Z W -5 -1 2 6 XY = β5 β (β1) XY = β5 + 1 XY = β4 XY = 4 ZY = 2 β (β1) ZY = 2 + 1 ZY = 3 ZY = 3 So ππ β ππ because XY = ZW ZW = 2 β 6 ZW= β4 ZW = 4 ZW = 4 BETWEEN In order to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC. A B C B is between A and C A C B B is not between A and C SEGMENT ADDITION POSTULATE 1-2-2 β’ If B is between A and C, then AB + BC = AC β’ Notice A, B and C must be collinear A B 3 A C 5 B C AB + BC = AC 3 + 5 = AC 8 = AC ANOTHER SEGMENT ADDITION POSTULATE EXAMPLE If MN = 2x β 6, NO = x + 7 and MO = 25, find the value of x. Then find MN and NO. M N MN + NO = MO 2x β 6 + x + 7 = 25 3x + 1= 25 3x = 24 x=8 O MN = 2x - 6 MN = 2(8) - 6 MN = 16-6 MN = 10 Check: MN + NO = MO remember MO = 25 10 + 15 = MO 25 = MO so it checks NO = x + 7 NO = 8 + 7 NO = 15 MIDPOINT β’ A point that divides the segment into two congruent segments R If given S is the midpoint of π π, then π π β ππ S T MIDPOINT EXAMPLES Given: Y is a midpoint of π΄π΅ If XY = 6 find YZ and XZ. YZ = 6 XZ = 2(6)=12 X If XZ = 20 find XY and YZ XY = 20 2 = 10 XZ = 10 (because XY = XZ) Y Z ANOTHER MIDPOINT EXAMPLE M is the midpoint of π π. Find RM, MT and RT. 5x + 9 8x - 36 R M T RM = TM 5x + 9 = 8x β 36 RM = 5x + 9 MT = 8x - 36 -3x +9 = -36 RM = 5(15) + 9 MT = 8(15) - 36 -3x = -45 RM = 75 + 9 MT = 120 - 36 x = 15 RM = 84 = MT = 84 RT = RM + MT RT = 84 + 84 RT = 168 SEGMENT BISECTOR Segment Bisectorβis any ray, segment, or line that intersects a segment at its midpoint. It divides the segment into two equal parts at its midpoint. D C A B π΅π· bisects π΄πΆ