1) Definition: Angle. 2) Sides of an angle. 3) Vertex of an angle

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1 Geometry Chapter 3 - Note Taking Guidelines Complete each Now try problem after studying the previous example 3.1 Angles and Their Measures 1) Definition: Angle 2) Sides of an angle 3) Vertex of an angle 4) Can angles be formed by segments? i) What should you always keep in mind about angles 5) The symbol for angle vs. the symbol for is less than 6) Three ways to name angles 7) Straight angles 8) Zero angles

2 9) Do we usually name straight angles or zero angles when working with figures 10) Other than the zero angle, all angles separate the plane into 11) Excluding straight angles an angle creates two sets which are... 12) Each nonzero angle has two parts 13) A straight angle is a unique case of the above two ideas. How? 14) The measure of an angle 15) The unit of measure used when measuring angles is often 16) The symbol for degrees 17) The notation for indicating the measure of an angle is

3 18) What is a degree? 19) Why is 360 used in the development of a degree 20) The measure of the exterior of an angle is 21) Typically the measure of an angle refers to 22) Postulate: Angle Measure i) Unique Measure Assumption ii) Unique Angle Assumption iii) Zero Angle Assumption iv) Straight Angle Assumption v) Angle Addition Property

4 23) Study example 1 24) Now try the following problem: 25) Definition: Angle Bisector 26) Study example 2 27) Now try the following problem: 28) Where is the measure of an angle placed in drawings? 29) Some of the assumptions that can be made from a diagram: 30) Some things you cannot assume from a diagram: Summarize what you learned in sections 3.1:

5 3.2 Arcs and Rotations 1) There is a close relationship between angles and 2) Describe the arc AB of a circle 3) What is the symbol for the arc AB of a circle? 4) What unit is used when measuring arcs? 5) Define: Central angle of a circle 6) Define: Minor arc 7) Define: Endpoints of an arc 8) Define: Major arc

6 9) Notation for a major arc vs. minor arc 10) Describe Semicircles 11) Definition: Degree measure of a minor arc or semicircle 12) Definition: Degree measure of a major arc 13) Study example 1 14) Now try the following problem: 15) Concentric circles 16) Arc length vs. Arc measure

7 17) Image 18) Preimage 19) Clockwise rotation in mathematics is considered 20) Counter clockwise rotation is considered 21) Magnitude of a rotation Summarize what you learned in sections 3.2:

8 3.3 Properties of Angles 1) Every angle has a unique measurement in the range 2) Definitions of types of angles: i) Zero ii) Acute iii) Right iv) Obtuse v) Straight 3) The symbol for a right angle is. 4) Definition: Complementary Angles 5) Definition: Supplementary Angles

9 6) The complement to an angle with measure x is 7) The supplement to an angle with measure x is 8) Study example 1 9) Now try the following problem: 10) Definition: Adjacent Angles 11) Study example 2 12) Now try the following problem: 13) The common side of adjacent angles must 14) Now try the following problem:

10 15) Definition of Linear Pair: 16) Theorem: Linear Pair 17) Study example 3 18) Now try the following problem: 19) Definition: Vertical Angles 20) Theorem: Vertical Angles 21) Study example 4 22) Now try the following problem: Summarize what you learned in sections 3.3:

11 3.4 Algebra Properties Used in Geometry 1) The properties of geometry are like 2) Three types of properties and the name for each 3) Postulates of Equality: i) Reflexive Property of Equality ii) Symmetric Property of Equality iii) Transitive Property of Equality 4) Postulates of Equality and Operations: i) Addition Property of Equality ii) Multiplication Property of Equality 5) Two angles labeled with the same arc indicates

12 6) Postulates of Inequality and Operations: i) Transitive Property of Inequality ii) Addition Property of Inequality iii) Multiplication Property of Inequality 7) Study example 2 8) Now try the following problem: a) Name the properties of inequality and operations that are used in solving 180 < 12m 30 9) Now try the following problem: a) Knowing that m X < m Y, what can you conclude about m X + m Z and m Y + m Z using the Addition Property of Inequality 10) Postulates of Equality and Inequality i) Equation to Inequality Property (The whole is greater than any of its parts) ii) Substitution Property Summarize what you learned in sections 3.4:

13 3.5 One-Step Proof Arguments 1) To prove a conditional, p => q, a proof writer provides a 2) Definition: Proof Argument 3) One-Step proofs 4) Justification for conclusion 5) Three types of justifications 6) Study example 1 7) Now try the following problem: 8) Study example 2 9) Now try the following problem:

14 10) To write justifications you need to be 11) Three reasons that proofs are important in mathematics.. 12) Now try the following problem: 13) Now try the following problem: Summarize what you learned in sections 3.5:

15 3.6 Parallel Lines 1) The tilt of a line 2) What is the grade of a road? 3) Define: Transversal 4) How many angles are formed by a transversal? 5) Define: Corresponding angles 6) Corresponding Angles Postulates: 7) Shorthand notation for the Corresponding Angles Postulates 8) Study example 1 9) Now try the following problem:

16 10) What term refers to the tilt of a line in the coordinate plane? 11) Definition: Slope 12) The slope is the change 13) The slope tells us how many units the line goes up or down 14) The slope of a horizontal line 15) The slope of a vertical line 16) The slope of an oblique line 17) Study example 2 18) Now try the following problem:

17 19) The slope of a line can be found 20) Study example 3 21) Now try the following problem: 22) Theorem: Parallel Lines and Slope 23) Shorthand for the Parallel Lines and Slope Theorem 24) All vertical lines are 25) Theorem: Transitivity of Parallelism Summarize what you learned in sections 3.6:

18 3.7 Perpendicular Lines 1) Definition: Perpendicular 2) The symbol for perpendicular 3) Now try the following problem: 4) Theorem: Two Perpendiculars 5) Use symbols to write the Two Perpendiculars Theorem: (Include a diagram) 6) Theorem: Perpendicular to Parallels 7) Use symbols to write the Perpendicular to Parallels Theorem: (Include a diagram)

19 8) Now try the following problem: 9) Theorem: Perpendicular Lines and Slopes 10) The exception to the above idea for vertical and horizontal lines 11) Now try the following problem: 12) Summary of Parallel and Perpendicular Lines Summarize what you learned in sections 3.7:

20 3.8 Drawing Parallel & Perpendicular Lines 1) Define: Bisector of a segment 2) Define: Perpendicular Bisector of a segment 3) Geometric Construction 4) The only two tools allowed in constructions 5) Now try the following problem: 6) above

21 7) Algorithm 8) Now try the following problem: (a) 9) Now try the following problem: Summarize what you learned in sections 3.8:

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