University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2021
Views:

385

Pages:

10
Author:

causentas5l7

2.2 Segment and Angle Addition Postulates (Structure of Geometry) warm up Z Y The figure shows three angles whose vertex is X. 1. Write two names for each angle. X W 2. Which two angles are adjacent. 3. Is Y in the interior or exterior of ? 2.2 the structure of geometry 1. I can use postulates and theorems relating points, lines, and planes to justify statements. 1 2.2 Segment and Angle Addition Postulates (Structure of Geometry) Postulates (axioms): Basic assumptions or statements that are accepted without proof The Ruler Postulate: The points on a line can be matched, onetoone with a set of real numbers (coordinates). 4 The distance between two points on a number line can be found by taking the absolute value of the difference of their coordinates. OR 2 2.2 Segment and Angle Addition Postulates (Structure of Geometry) Segment Addition Postulate: On if B is between A and C, then AB + BC = AC Example 1: Example 2: Given that SG = 20, find the following: 3 2.2 Segment and Angle Addition Postulates (Structure of Geometry) Example 3: If C and D are in plane P, then the measure of is equal to the absolute value of the difference between the real numbers for and Example 4: find 4 2.2 Segment and Angle Addition Postulates (Structure of Geometry) Angle Addition Postulate: If C is in the interior of then Also: The Protractor Postulate: On in a given plane, P, choose any point O between A and B. Consider and on the same side of (opposite rays) and all the rays that can be drawn from O These rays can be paired with real numbers from 0 to 180 inclusive 5 2.2 Segment and Angle Addition Postulates (Structure of Geometry) Example 5: 6 2.2 Segment and Angle Addition Postulates (Structure of Geometry) Example 6: 7 2.2 Segment and Angle Addition Postulates (Structure of Geometry) 8 2.2 Segment and Angle Addition Postulates (Structure of Geometry) classwork Work with a partner or small group to complete the following problems in the textbook: Page 6769 #1122 all, #3742 all 9 2.2 Segment and Angle Addition Postulates (Structure of Geometry) recap Ruler Postulate 1. The ________ ___________ says that points on a line can be matched onetoone with the real numbers. Postulates are basic assumptions that are accepted without proof. 2. ___________ 3. AC = x + (x+6) is an example of the Segment Addition Postulate ________ ___________ __________ Protractor __________ Postulate says that rays extending from a common 4. The _________ vertex on the same side of a line containing the vertex can be paired with real numbers from 0 to 180. exit ticket 1. Explain how you think the Segment Addition Postulate could be used in real life. 2. Sketch and label the following objects: a. A point exterior to an obtuse angle b. The midpoint of the segment joining (0,2) and (4,6) 10