Chapter 1 Introduction to Geometry

Slide Getting Started Points – To name a point always use Lines – All lines are and extend in both directions. To name a line use on the line. Line Segment – Has a definite and, called. To name a segment use. Ray – Begins at and then extends in one direction. To name a ray you must name the first and then on the ray.

Slide Getting Started Angle – Two with the same form an angle. The common is called the, and the two are called the. Triangle –To name a triangle use of the triangle. Union ( ) – What do the objects ? Intersection (∩) – What do the objects ?

Slide Example

Slide Measurement of Segments and Angles Measuring Segments Find AB. Classifying Angles Acute: Angle measures Right: Angle measures Obtuse: Angle measures Straight: Angle measures

Slide Measurement of Segments and Angles Measuring Angles 60 minutes = 60 seconds = Congruent ( ) Two angles with the Two segments with the On diagrams we use to indicate congruent parts.

Slide Examples

Slide Examples

Slide Collinearity, Betweenness, and Assumptions Collinear – Points that lie on Noncollinear – Points that Betweenness of Points – All three points must be Triangle Inequality – The sum of the lengths of any is always than the length of the You should assume from a diagram… 1) Straight lines and angles 2) Collinearity of points 3) Betweenness of points 4) Relative positions of points

Slide Examples

Slide Examples

Slide Beginning Proofs StatementsReasons Theorem – A mathematical model that can be.

Slide Examples StatementsReasons

Slide Examples StatementsReasons

Slide Division of Segments and Angles Bisect – Divide a segment or angle into parts On a segment the bisection point is called the. In an angle, the dividing ray is called the. Trisect – Divide a segment or angle into parts On a segment, the two points that divide the segment are called. In an angle, the two dividing rays are called.

Slide Examples StatementsReasons

Slide Examples StatementsReasons

Slide Examples StatementsReasons

Slide Deductive Structure & 1.8 Statements of Logic Conditional Statement: If p, then q. Hypothesis: Conclusion: Negation: Every conditional statement has three other statements. 1.Converse – hypothesis and conclusion 2.Inverse – hypothesis and conclusion 3.Contrapositive – hypothesis and conclusion Theorem 3: If a conditional statement is true, then the of the statement is also true.

Slide & 1.8 Examples If Joe is a member of the RB soccer team, then he is a student at RB. 1)Write the converse. 2) Write the inverse. 3) Write the contrapositive. 4) Are the above statements true?

Slide & 1.8 Examples What conclusion can you draw given:

Slide Probability

Slide Example