9Segments and Their Measures 1.3Segments and Their Measures
101.3 Postulate 1- The Ruler Postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point.The Distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B.AB is also called the length of AB.AB
111.3 Postulate 2: Segment Addition Postulate If B is between A and C, then AB+BC=AC.If AB+BC=AC, then B is between A and C.ACB
12Distance FormulaIf A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B isAB= (x2-x1) 2 + (y2-y1)2
13Using the Distance Formula Use the Distance Formula to find the lengths between the two points.A(-1,1) B(-4,3)Try and then we will check it..
14ANSWER DID YOU GET IT CORRECT? AB= (x2-x1) 2 + (y2-y1)2 ((-4)- (-1))2 +(3-1) 2(-3)2 +229+413DID YOU GET IT CORRECT?
15Now your turn to try it… AE=20 BD=6 AB=BC=CD In the picture of collinear points,AE=20BD=6AB=BC=CDDFind Each Length…BCABACADC3BA369
16Angles and Their Measures 1.4Angles and Their Measures
18What are the two names of the angle? Naming AnglesWhat are the two names of the angle?CAL ABC and L CBAB
191.4 Postulate 3: Protractor Postulate Consider a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180. The measure of L AOB is equal to the absolute value of the difference between the real numbers for OA and OB.ABO
201.4 Postulate 4: Angle Addition Postulate If P is in the interior of L RST, thenmLRSP+mLPST=mLRSTRmLRSTmLRSPSPmLPSTT
21An angle with a measure between 0 degrees and 90 degrees Acute AngleAn angle with a measure between 0 degrees and 90 degrees
22An angle with a measure of 90 degrees. Right AngleAn angle with a measure of 90 degrees.
23An angle with a measure between 90 degrees and 180 degrees. Obtuse AngleAn angle with a measure between 90 degrees and 180 degrees.
24An angle with a measure of 180 degrees. Straight AngleAn angle with a measure of 180 degrees.
25Adjacent AnglesTwo angles with a common vertex and side, but no common interior points.
26Now your Turn Using the Angle Addition Postulate. What is mLDBC? Answer:30°A60°DBC
27Segment and Angle Bisectors 1.5Segment and Angle Bisectors
28(x1,y1) (x2,y2) Midpoint Formula If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the midpoint of AB has coordinates.(x1,y1)(x2,y2)
29Your turn Applying Midpoint Formula Find the midpoint of AB.A(-2,3) and B(5,-2)ANSWER 3, 12 2
31Vertical Angles/ Linear Pair Consists of two angles whose sides form two pairs of opposite rays.Consists of two adjacent angles whose non-common sides are opposite rays.56L1 and L3 are vertical angles.L2 and L4 are vertical angles.L5 and L6 are linear pairs
32Finding the Angle Measure… Find the Measurement of L1.Answer: 150°30°1Answer: 45°45°1