9 Segments and Their Measures 1.3Segments and Their Measures
10 1.3 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
11 1.3 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
12 Distance 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
13 Using 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..
14 ANSWER 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?
15 Now 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
16 Angles and Their Measures 1.4Angles and Their Measures
18 What are the two names of the angle? Naming AnglesWhat are the two names of the angle?CAL ABC and L CBAB
19 1.4 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
20 1.4 Postulate 4: Angle Addition Postulate If P is in the interior of L RST, thenmLRSP+mLPST=mLRSTRmLRSTmLRSPSPmLPSTT
21 An angle with a measure between 0 degrees and 90 degrees Acute AngleAn angle with a measure between 0 degrees and 90 degrees
22 An angle with a measure of 90 degrees. Right AngleAn angle with a measure of 90 degrees.
23 An angle with a measure between 90 degrees and 180 degrees. Obtuse AngleAn angle with a measure between 90 degrees and 180 degrees.
24 An angle with a measure of 180 degrees. Straight AngleAn angle with a measure of 180 degrees.
25 Adjacent AnglesTwo angles with a common vertex and side, but no common interior points.
26 Now your Turn Using the Angle Addition Postulate. What is mLDBC? Answer:30°A60°DBC
27 Segment 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)
29 Your turn Applying Midpoint Formula Find the midpoint of AB.A(-2,3) and B(5,-2)ANSWER 3, 12 2
31 Vertical 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
32 Finding the Angle Measure… Find the Measurement of L1.Answer: 150°30°1Answer: 45°45°1