2.6 Deductive Reasoning GEOMETRY.

Slides:

Advertisements

Similar presentations

2-8: Proving Angle Relationships

Advertisements

More Angle Relationships. Deductive Reasoning To deduce means to reason from known facts When you prove a theorem, you are using deductive reasoning using.

2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.

Section 1.6 Pairs of Angles

2.3 Complementary and Supplementary Angles

Angle Pair Relationships

Angle Relationships Section 1-5 Adjacent angles Angles in the same plane that have a common vertex and a common side, but no common interior points.

Conjectures that lead to Theorems 2.5

Chapter 2.7 Notes: Prove Angle Pair Relationships

SPECIAL PAIRS OF ANGLES. Congruent Angles: Two angles that have equal measures.

Chapter 2.7 Notes: Prove Angle Pair Relationships Goal: You will use properties of special pairs of angles.

2.4 Vertical Angles. Vertical Angles: Two angles are vertical if they are not adjacent and their sides are formed by two intersecting lines.

Geometry Section 1.5 Describe Angle Pair Relationships.

L.T. I can identify special angle pairs and use their relationships to find angle measure.

Geometry Section 1.6 Special Angle Pairs. Two angles are adjacent angles if Two angles are vertical angles if.

Angle Relationships Geometry 1.5.

Prove Theorems Advanced Geometry Deductive Reasoning Lesson 4.

P. 114: 23 – 28. Given Transitive prop. congruence Definition of congruence Given Transitive prop. Equality/Substitution.

1.4 Pairs of Angles Adjacent angles- two angles with a common vertex and common side. (Side by side) Linear pair- a pair of adjacent angles that make a.

1.5 Exploring Angle Pairs.

2-4 Special Pairs of Angles Objectives -Supplementary Angles Complementary Angles -Vertical angles.

Section 1-6 Angle Pair Relationships. Vertical angles Formed when two lines intersect. Vertical Angles are Congruent. 1 2.

Honors Geometry Section 1.3 part2 Special Angle Pairs.

3.2 Proof and Perpendicular Lines

2.4: Special Pairs of Angles

1-3 Pairs of Angles.

Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

ANGLERELATIONSHIPS SECTION 1-5 and 2-8 Jim Smith JCHS Spi.3.2.E.

Pairs of Angles Geometry Farris O I can identify adjacent, vertical, complementary, and supplementary angles. I can find measures of pairs of angles.

Any two angles whose sum is 180 degrees. Supplementary Angles.

Geometry 1.6 Angle Pair Relationships. VERTICAL ANGLES Vertical angles are two angles whose sides form two pairs of opposite rays

2-4 Special Pairs of Angles. A) Terms 1) Complementary angles – a) Two angles whose sum is 90° b) The angles do not have to be adjacent. c) Each angle.

Proving the Vertical Angles Theorem (5.5.1) May 11th, 2016.

+ CHAPTER 2 Section 4: Complementary and Supplementary Angles.

Lesson 1-5: Pairs of Angles

Congruent Angles.

Chapter 2 Reasoning and Proof.

Chapter 1 section 7 Angle relationships

Special pairs of angles

2.8 Notes: Proving Angle Relationships

Chapter 1: Essentials of Geometry

Angle Pairs More Angle Pairs Definitions Pictures Angles

1.5 Exploring Angle Pairs.

Chapter 1.5 Notes: Describe Angle Pair Relationships

Angle Relationships Section 1-5.

Statements About Segments and Angles

Section 1.5. Section Angle Pair Relationships Identify vertical angles and linear pairs. Identify complementary and supplementary angles.

Types of Angles & Their Relationships

Adjacent, Vertical, Supplementary, and Complementary Angles

Describe Angle Pair Relationships

1.6 Angle Pair Relationships

Angle Pairs Module A1-Lesson 4

2.6 Proving Statements about Angles

1-5 Angle Relations.

Angle Pair Relationships

Chapter 2 Section 4 Special Angle Pairs Special Angle Pair #1:

X = 6 ED = 10 DB = 10 EB = 20 Warm Up.

Angle Pair Relationships

2.6 Proving Statements about Angles

Special Pairs of Angles

Describe Angle Pair Relations

Lesson 1-5 Pairs of Angles.

Chapter 1 Basics of Geometry.

Goal: The learner will use properties of special pairs of angles.

Exploring Angle Pairs Skill 05.

Proving Statements about Angles

Adjacent Angles Definition Two coplanar angles with a common side, a common vertex, and no common interior points. Sketch.

Identifying Angle Pair Relationships

Geometry Exploring Angle Pairs.

Presentation transcript:

2.6 Deductive Reasoning GEOMETRY

Special Pairs of Angles Vertical angles Linear pair of angles Complementary angles Supplementary angles

Vertical Angles Definition: If two angles have their sides that form two pairs of opposite rays, then the two angles are vertical angles. VERTICAL ANGLES THEOREM: If two angles are vertical angles, then they are congruent.

Linear Pair Definition: If two angles are adjacent and their noncommon Sides are opposite rays, then the two angles form a linear pair. LINEAR PAIR POSTULATE: If two angles for a linear pair, then They are supplementary The sum of their measures is 180o.

Complementary Angles Definition: If two angles have a sum of 90o, then the two angles are complementary angles. Each angle is the complement of the other. The angles themselves do not have to be adjacent, but if they are, they must form a “perfect” corner.

Congruent Complements Theorem If two angles are complementary to the same or to congruent angles, Then the two angles are congruent. If A and B are complementary and C and B are complementary then A  C because both A and C are complementary to B.

Supplementary Angles Definition: If two angles have a sum of 180o, then the two angles are complementary angles. Each angle is the supplement of the other. The angles themselves do not have to be adjacent, but if they are, they must form a straight line.

Congruent Supplements Theorem If two angles are supplementary to the same or to congruent angles, Then the two angles are congruent. If A and B are supplementary and C and B are supplementary then A  C because both A and C are supplementary to B.