Ch 5.6.  We will look at the properties of the Hinge Theorem.  Learn a new kind of proof.

Slides:



Advertisements
Similar presentations
Sec 2-6 Concept: Proving statements about segments and angles Objective: Given a statement, prove it as measured by a s.g.
Advertisements

Honors Geometry Section 4.6 (1) Conditions for Special Quadrilaterals
Chapter 5: Relationships Within Triangles 5.4 Inverses, Contrapositives, and Indirect Reasoning.
Inequalities in Two Triangles
Sara Wunderlich. Describe what a perpendicular bisector is. Explain the perpendicular bisector theorem and its converse. Give 3 examples of each. Perpendicular.
Chapter 5 Perpendicular Bisectors. Perpendicular bisector A segment, ray or line that is perpendicular to a segment at its midpoint.
Geometry Chapter 5 Benedict. Vocabulary Perpendicular Bisector- Segment, ray, line or plane that is perpendicular to a segment at its midpoint. Equidistant-
PROPERTIES AND ATTRIBUTES OF TRIANGLES
5.2 Bisectors of Triangles5.2 Bisectors of Triangles  Use the properties of perpendicular bisectors of a triangle  Use the properties of angle bisectors.
Ch 5.3 Use Angle bisectors of triangles. In this section… We will use the properties of an angle bisector to solve for missing side lengths.
Katerina Palacios The perpendicular bisector theorem states that if one point lies on the perpendicular bisector of a segment then it is equidistant.
 Perpendicular bisector – is a line that goes through a segment cutting it into equal parts, creating 90°angles  Perpendicular bisector theorem – if.
By: Ana Cristina Andrade
Pythagorean Theorem step by step a c b Picture This!
Chapter 5 Relationships within Triangles In this chapter you will learn how special lines and segments in triangles relate.
Relationships within Triangles Chapter Midsegment Theorem and Coordinate Proof Midsegment of a Triangle- a segment that connects the midpoints.
A perpendicular bisector is a a line that intersects at the midpoint of a segment forming four 90 degree angles. Perpendicular Bisector theorem: If there.
Proof Geometry.  All quadrilaterals have four sides.  They also have four angles.  The sum of the four angles totals 360°.  These properties are.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm up 1) Find 4.5 Proving Quadrilateral Properties W Y X 2x-6 40°
Logical Reasoning:Proof Prove the theorem using the basic axioms of algebra.
P. 270 #47-49.
Bisectors of a Triangle
Bisectors in Triangles Section 5-2. Perpendicular Bisector A perpendicular tells us two things – It creates a 90 angle with the segment it intersects.
Ch 1.6 Commutative & Associative Properties
Perpendicular Bisectors of a Triangle Geometry. Equidistant A point is equidistant from two points if its distance from each point is the same.
Bisectors in Triangles Chapter 5 Section 3. Objective Students will identify properties of perpendicular bisectors and angle bisectors.
5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify.
Friday, November 9, 2012 Agenda: TISK; No MM. Lesson 5-6: Compare side lengths and measures using the Hinge Theorem. Homework: 5-6 Worksheet.
3.4 Proofs with Perpendicular Lines. Finding the Distance from a Point to a Line The length of a perpendicular segment from a point to a line is considered.
Bellwork Write if-then form, converse, inverse, and contrapositive of given statement. 3x - 8 = 22 because x = 10.
5-5 Indirect Proof. Indirect Reasoning: all possibilities are considered and then all but one are proved false. The remaining possibility must be true.
5.5 Indirect Reasoning -Indirect Reasoning: All possibilities are considered and then all but one are proved false -Indirect proof: state an assumption.
Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,
Perpendicular and Angle Bisectors Perpendicular Bisector – A line, segment, or ray that passes through the midpoint of a side of a triangle and is perpendicular.
Using Properties of Parallel Lines Sec. 3.5 p. 157 GOAL: To use properties of parallel lines.
Chapter 5 Lesson 3 Objective: Objective: To identify properties of perpendicular and angle bisectors.
Bisectors in Triangles Concurrency of Perpendicular Bisector Theorem If the perpendicular bisectors PX, PY and PZ are concurrent at P, then PA = PC = PB.
EXAMPLE 3 Write an indirect proof Write an indirect proof that an odd number is not divisible by 4. GIVEN : x is an odd number. PROVE : x is not divisible.
Lesson: Objectives: 6.5 Squares & Rhombi  To Identify the PROPERTIES of SQUARES and RHOMBI  To use the Squares and Rhombi Properties to SOLVE Problems.
Proofs. Warm Up Using the diagram below, create a problem to give to your partner – For example, what kind of angles are “blah” and “blah” – Or, if m
Midsegment Theorem and Coordinate Proofs
Isosceles and Equilateral Triangles
Unit 2 – Similarity, Congruence, and Proofs
Warm-up Solve for x x x-3 4 x+6 x+1 x
5.1 Midsegments of Triangles
3.1 Indirect Proof and Parallel Postulate
Parallel Lines & Angle Relationships
5.6 Indirect Proof and Inequalities in Two Triangles
Section 11-7 Ratios of Areas.
Special Parallelograms
Bell Ringer Mrs. Rivas Nancy wrote a proof about the figure shown below. In the proof below, Nancy started with the fact that
Date: Topic: Rhombi, Rectangles, and Squares (7.2)
Bisectors in Triangles
Direct Proof and Counterexample I
An indirect proof uses a temporary assumption that
Special Parallelograms
Proofs.
6 Vocab Review: Backs to Front
Math Humor What kind of roots does a geoma tree have? Square Roots!!!!
Unit 5: Geometric and Algebraic Connections
Inequalities in Two Triangles
Bisectors of a Triangle
Y. Davis Geometry Notes Chapter 5.
Properties of Triangles
Check your work from yesterday with the correct answers on the board.
Inequalities in Two Triangles
5.2 Bisectors of Triangles
9-6: Rhombus, Rectangle, and Square
Bisectors of a Triangle
Presentation transcript:

Ch 5.6

 We will look at the properties of the Hinge Theorem.  Learn a new kind of proof.

ACB

 In an indirect, you assume that whatever you want to prove is false and then find a counterexample. Yeah, we are learning another kind of proof.

 Prove: All even numbers are divisible by 2.  Prove: All squares are quadrilaterals.  Prove: All perpendicular bisectors do not intersect inside a triangle.

 Given: x is a perfect square.  Prove: The square root of x is a whole number.