Section 2.1 Exploring Patterns.  Reasoning in geometry consists of 3 stages: (1)Look for a pattern (2)Make a conjecture – a guess as to what you think.

Slides:

Advertisements

Similar presentations

Proving Statements in Geometry

Advertisements

Defined Terms and Postulates April 3, Defined terms Yesterday, we talked about undefined terms. Today, we will focus on defined terms (which are.

1.1 Statements and Reasoning

Geometry Review Test Chapter 2.

4-7 Median, Altitude, and Perpendicular bisectors.

a location in space that has no size.

Vocabulary 2.1 MA418 – Spring 2010 McAllister. Point Location in space that has no size or dimension Is usually denoted by a dot and a capital letter.

Basic Definitions in Geometry

1.2 Points, Lines, and Planes 9/10/12

Basics of Geometry POINTS! LINES! PLANES!.

What’s on the Menu Today?

Line and Angle Relationships

Introduction to Angles

California State Standards 1. Understand and Use undefined terms, axioms, theorems, and inductive and deductive reasoning 15. Use the Pythagorean Theorem.

Geometry Ch 1.1 Notes Conjecture – is an unproven statement that is based on observation Inductive Reasoning – is a process used to make conjectures by.

§2.1 Introductory Material The student will learn about: and the beginning postulates to be used in this course. definitions of basic terms, 1.

 Give an example of a point, line and plane that can be found in the classroom.

Section 1.1 Undefined Terms: Point, Line, and Plane Point - Line - Plane -

Chapter 4 Congruent Triangles In this chapter, you will: classify triangles by their parts, apply the Angle Sum Theorem and the Exterior Angle Theorem,

Angles and Their Measures

Points, Lines, and Planes Sections 1.1 & 1.2. Definition: Point A point has no dimension. It is represented by a dot. A point is symbolized using an upper-case.

Triangles and Angles Sec 4.1 GOALS: To classify triangles by their angles and sides To find missing angle measures in triangles.

Copyright © 2009 Pearson Education, Inc. Chapter 9 Section 1 – Slide 1 AND.

Basics of Euclidean Geometry Point Line Number line Segment Ray Plane Coordinate plane One letter names a point Two letters names a line, segment, or ray.

Do Now 4/2/13 Take out HW from last night. Take out HW from last night. Text p. 312, #1-16 all, 21 Text p. 312, #1-16 all, 21 Copy HW in your planner.

Section 1-4 Angles and their Measures. Angle Formed by two rays with a common endpoint –T–The rays are the sides of the angle –T–The common endpoint is.

1.6 Angles and Their Measures

Angle Measure Section 1-4. angle – a figure consisting of 2 noncollinear rays with a common endpoint. The 2 rays are called the sides of the angle. The.

1.4 Measure and Classify Angles. Definitions Angle – consists of two different rays with the same endpoint. B C vertex The rays are the sides of the angle.

Answers to homework (page 11 in packet) problems

4.1 Triangles and Angles. 2 Standard/Objectives: Objectives: Classify triangles by their sides and angles. Find angle measures in triangles DEFINITION:

Basics of Geometry Defining Terms

1-6: Exploring Angles Expectation:

Warm - Up Solve the equations: 1. (1/2)x - 7 = x - 9 = 5x + 15.

+ Introduction to Angles. + Introduction to Lesson The purpose of this tutorial is to introduce angles and the various relationships they have. Upon completion.

Chapter 1Section 1 - Points and Lines in the Plane 1 Chapter 1 Exploring Geometry: Points, Lines, and Angles in the Plane Section 1 Points and Lines in.

Notes #2 (1.4) 1.4 Angles Measure

M217 Section 1.3 Measuring Angles. Angle Terminology: Angle: 2 different rays with the same endpoint Vertex: Common endpoint - A Sides: Two rays – Naming:

Date: Topic: Types of Angles (6-2) An angle is the union of two rays with a common endpoint. The endpoint is the vertex of the angle, and each ray is a.

Geometry Chapter 2 REASONING. Geometry Chapter 2 : REASONING Exploring Patterns The structure of geometry Segment and Angle relationships Conditional.

Basics of Geometry Chapter Points, Lines, and Planes Three undefined terms in Geometry: Point: No size, no shape, only LOCATION.  Named by a single.

Welcome to Geometry Unit 1 Vocabulary. Undefined Terms Point In Euclidean geometry, a point is undefined. You can think of a point as a location. A point.

LESSON 2 UNDEFINED TERMS. In Geometry, there are 3 undefined terms: points, lines, and planes. We can give descriptions of these three terms. We also.

Section 10.1 Points, Lines, Planes, and Angles Math in Our World.

1-4: Measuring Angles. Parts of an Angle Formed by the union of two rays with the same endpoint. Called sides of the angle Called the vertex of the angle.

Triangles and Their Angles Geometry – Section 4.1.

Slide 1-1 Copyright © 2014 Pearson Education, Inc. 1.3 Segments, Rays and Angles.

Warm Up If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

Foundations of Geometry

Section 9.1 Points, Lines, Planes, and Angles

Triangle Fundamentals

Basics of Geometry POINTS! LINES! PLANES! OH MY!.

Chapter 1 Basics of Geometry.

Chapter 1 Basics of Geometry.

Triangle Fundamentals

4.1 Triangles and Angles.

4-1 Triangles HONORS GEOMETRY.

Triangle Fundamentals

TRIANGLES C.N.Colón Geometry St. Barnabas H.S. Bronx, NY.

Line and Angle Relationships

Basic Definitions G.CO.1 and G.CO.12 Objectives 1, 3, 6.

Section 9.1 Points, Lines, Planes, and Angles

Triangle Fundamentals

Basics of Geometry POINTS! LINES! PLANES! OH MY!.

4.1 Triangles and Angles October 6, 2011.

Chapter 4 Congruent Triangles.

Do Now 3/15/12 Take out HW from last night. Copy HW in your planner.

Naming Triangles Triangles are named by using its vertices.

Presentation transcript:

Section 2.1 Exploring Patterns

 Reasoning in geometry consists of 3 stages: (1)Look for a pattern (2)Make a conjecture – a guess as to what you think is happening (3) Verify the conjecture – use logical reasoning to verify that it is true in ALL cases.  First 2 steps are inductive reasoning. The third step is when you are proving it.

Important Definitions: Undefined terms: Point, Line, and Plane Line Segment: AB consists of the endpoints A and B and all points on line AB that lie between A and B. Line segment AB or BA

Defns cont.

Opposite rays CA and CB A C B Points, segments, or rays that lie on the same line are collinear. In the line above, the following are collinear: A,B,C ; AC, CB, AB ; AC, CB, BC

 An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The angle that consists of the rays AB and AC is denoted by <BAC, <CAB, or <A. The point A is the vertex of the angle.

 The measure of <A is denoted by m<A. Angles are classified as acute, right, obtuse, and straight. Right : m<A = 90 o Acute : 0 o < m<A < 90 o Obtuse : 90 o < m<A < 180 o Straight : m<A = 180 o

 Interior – a point is on the interior of an angle if it lies in between the points that lie on each side of the angle.  exterior – lies on the outside of the sides of the angle.

 Two angles are adjacent if they share a common vertex and side, but have no common interior points.  Angle ABC is adjacent to angle CBD Because: they have a common side (line CB) they have a common vertex (point B)