Inequalities in Two Triangles

Slides:

Advertisements

Similar presentations

Lesson 5 – 6 Inequalities in Two Triangles

Advertisements

CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve.

Chapter 5: Inequalities!

5-7 Inequalities in Two Triangles

Triangle Inequalities

Math I Unit 3 Concept: Triangular Inequalities The Hinge Theorem.

The Hinge Theorem Sec 5.6 Goal: To use the hinge theorem.

5.7 Inequalities in Two Triangles

1 Inequalities In Two Triangles. Hinge Theorem: If two sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the.

Jeopardy Triangle Sides Triangle Inequality Hinge Theorem Converse of Hinge Theorem Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500.

5.6 Indirect Proof and Inequalities in Two triangles.

Honors Geometry Section 4.8 Triangle Inequalities

Isosceles and Equilateral Triangles Chapter 4 Section 5.

Use Isosceles and Equilateral Triangles

Honors Geometry Section 4.4 Isosceles Triangle Theorem

11/18/09 Do Now Have your homework out on your desk. Find all of the angle measures below.

5-6 Inequalities in One Triangle

Triangle Congruence by ASA and AAS Chapter 4 Section 3.

5.6 Inequalities in One Triangle The angles and sides of a triangle have special relationships that involve inequalities. Comparison Property of Inequality.

Congruence in Right Triangles Chapter 4 Section 6.

Classify triangles by sides No congruent sides Scalene triangle At least two sides congruent Isosceles triangle Three congruent sides Equilateral triangle.

 Earlier in this chapter, we looked at properties of individual triangles using inequalities.  We know that the largest angle is opposite the longest.

5-5 Indirect Proof. Indirect Reasoning In indirect reasoning, all possibilities are considered and then all but one are proved false. – The remaining.

Triangle Sum Theorem The sum of the angle measures in a triangle is 180 degrees.

4.7 Triangle Inequalities. In any triangle…  The LARGEST SIDE lies opposite the LARGEST ANGLE.  The SMALLEST SIDE lies opposite the SMALLEST ANGLE.

Pythagorean Theorem and Its Converse Chapter 8 Section 1.

CHAPTER 4 SECTION 2 Triangle Congruence by SSS and SAS.

Chapter 5.5 Inequalities in Triangles. Property: Comparison Property of Inequality If a = b+c and c > 0, then a > b Proof of the comparison property –

Geometry Section 5.5 Use Inequalities in a Triangle.

Chapter 5: Relationships Within Triangles 5.5 Inequalities in Triangles.

5.7 Inequalities in Two Triangles

4.7 Triangle Inequalities

Analyzing Isosceles Triangles Chapter 4, Section 6.

Lesson 5.5 Inequalities Involving Two Triangles. SAS Inequality TheoremSSS Inequality Theorem (Hinge Theorem) - When 2 sides of a triangle are congruent.

Parallel Lines and Triangles Chapter 3 Section 5.

5.6 Notes Inequalities in One Triangle. Comparison Property of Inequality.

Properties of Rhombus, Rectangles, and Squares Chapter 6 Section 4.

4-2 Triangle Congruence by SSS and SAS

Proving Triangle Similarity by SSS and SAS

Inequalities in two triangles

Proving Triangles Congruent: SSS and SAS

Chapter 6 Inequalities in Geometry page 202

5.7 Inequalities in Two Triangles

Inequalities in Two Triangles

5.6: Inequalities in Two Triangles and Indirect Proof

Inequalities for Two Triangles

Converse of Hinge Theorem

Section 5.6 Inequalities in Two Triangles

BASIC GEOMETRY Section 5.6: Inequalities in 2 Triangles

Proving Triangles Congruent

6.5 & 6.6 Inequalities in One and Two Triangle

Exploring– Open your workbooks to P. EXPLORE!!!

5-6 Inequalities in Two Triangles

Inequalities for One Triangle

Inequalities in 2 triangles

6.5 & 6.6 Inequalities in One and Two Triangle

Proving Triangles Similar.

Section 20.4: SSS Triangle Congruence

BASIC GEOMETRY Section 5: Inequalities in one Triangle

Base Angles & Exterior Angles

Proving Triangles Similar.

Inequalities in Two Triangles

T H E O R M S TRIANGLES CONCEPT MAP Prove Triangles are Congruent

GEOMETRY 5.5 INEQUALITIES involving 2 Triangles Pages: 273 – 275

Advanced Geometry Section 3.7 The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive Learner Objective: Students will solve proofs and problems.

Lesson 3-2 Isosceles Triangles.

Section 5-5 Inequalities in triangles

Inequalities in Two Triangles

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

Inequalities in Two Triangles Chapter 5 Section 7

Objective Students will apply inequalities in two triangles. This means that students will use angle side relationships to solve problems in two triangles.

The Hinge Theorem (5-3) If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle. Also known as SAS Inequality Theorem

Turn to page 333… Look at problem 1 and Problem 2 Try the “Got It” problem at the bottom of each example.

Converse of the Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side. Also known as the SSS Inequality Theorem

Turn to Page 335… Look at Problem 3 and 4 Try the “Got It” problems at the bottom of each example.

On page 336… Try problems #1-5 on your own

Continue on page 336… Complete problems #6-18.

Reflection Explain in your own words the Hinge Theorem. How can this help you to solve problems? Explain in your own words the Converse of the Hinge Theorem. How are the two different?