Geometry Concepts and Postulates

Explore key concepts in geometry including definitions of postulates and theorems, the Segment Addition Postulate, and the Protractor Postulate. Learn how to apply these principles to solve problems and determine lengths and angles within geometric figures.

• Geometry
• Postulates
• Theorems
• Segments
• Angles

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1. Section 2.2 Structure of Geometry

2. Definitions Postulate(axiom)- is a statement accepted without proof Theorem-is a statement that is proven by using defs, postulates, or previously proven theorems

3. Postulates: Ruler Postulate- the pts on a # line can be paired 1:1 with the set of reals # s(coords) and the distance between any 2 pts = diff of their coords Ex: A B -6 4 d AB= -6 4 = 10 units

4. Example : Find the distance from A to B: A B 3 8 AB = 8 3 = 5

5. Segment Addition Postulate- Pts A, B, & C are collinear and B is in between A & C, then AB + BC = AC ( 2parts sum= whole) If B is between A and C, then AB + BC = AC A B C

6. S is between T and V. R is between S and T. T is between R and Q. QV = 18, QT= 6, TR=RS=SV. Make a sketch and answer. Find 1. RS 2. QS 3. TS 4. TV

7. Suppose J is between H and K. Use the segment Addition Postulate to solve for x. Then find the length of each segment. 1. HJ = 2x + 4 JK = 3x + 3 KH = 22 2. HJ = 5x -3 JK = 8x - 9 KH = 131 3. HJ = 2x + 1/3 JK = 5x + 2/3 KH = 12x - 4

8. Protractor Postulate- the rays of a given angle can be paired 1:1 on the protractor and the measure is determined by: diffs of those real # s

9. Angle addition Postulate- If C is in the interior of <AOD, then m<AOC + m<COD = m<AOD.

11. Q is in the interior of <ROS. S is in the interior of <QOP. P is in the interior of <SOT. S is in the interior of <ROT and m<ROT= 160 . M<SOT = 100 and m<ROQ = m<QOS = m<POT. Make a sketch and answer the following: 1. find m<QOP 2. m<QOT 3. m<ROQ

13. Let Q be in the interior of <POR. Use the angle addition Postulate to solve for x. Find the measure of each angle. 1. m<POQ = (X + 4) m<QOR = (2x 2) m<POR = 26 2. m<POQ = (3x + 7) m<QOR = (5x 2) m<POR = 61