Lesson 7.4 Inequalities pp. 281-286.

Slides:

Advertisements

Similar presentations

Warm-up Solve: 1) 2x + 1+4x +4x-11= 180 Compare greater than >, less than < or equal = 4+5___ 9 5+5__ 9 Find a number x. 6

Advertisements

5-3 Inequalities in One Triangle

CHAPTER 6: Inequalities in Geometry

Geometry 5-5 Inequalities in Triangles Within a triangle: – the biggest side is opposite the biggest angle. – the smallest side is opposite the smallest.

Triangle Inequality Theorem:

Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle.

Inequalities in One Triangle

Triangle Inequality Theorems Sec 5.5 Goals: To determine the longest side and the largest angle of a triangle To use triangle inequality theorems.

Chapter 5: Inequalities!

Geometry Chapter 5 Benedict. Vocabulary Perpendicular Bisector- Segment, ray, line or plane that is perpendicular to a segment at its midpoint. Equidistant-

5-7 Inequalities in Two Triangles

Triangle Inequalities

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

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.

A B C 12 We know ∠B = ∠C S TU 1214 We could write a proof to show ∠T ≠∠U *We could also prove that m ∠T > m ∠U, BUT theorem 1 tells us that!

Unit 2 Triangles Triangle Inequalities and Isosceles Triangles.

Triangle Inequality Theorem.  The sum of the two shorter sides of any triangle must be greater than the third side. Example: > 7 8 > 7 Yes!

Section 5-5: Inequities in Triangles March 8, 2012.

Bell Problem Find the value of x Use Inequalities in a Triangle Standards: 1.Analyze properties of 2-D shapes 2.Understand how mathematical ideas.

Use Inequalities in A Triangle

Triangle Inequalities

4.6 Congruence in Right Triangles In a right triangle: – The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle.

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

4.7 Triangle Inequalities. Theorem 4.10 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than.

The Triangle Inequality Thm. & Inequalities Involving 2 Triangles Section 5-4 and 5-5.

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

Chapter 7 Geometric Inequalities Chin-Sung Lin. Inequality Postulates Mr. Chin-Sung Lin.

Geometry Section 5.5 Use Inequalities in a Triangle.

4.7 Triangle Inequalities

Lesson 5.5 Use Inequalities in a Triangle. Theorem 5.10 A B C 8 5 IF AB > BC, THEN C > A The angle opposite the longest side is the largest angle; pattern.

Homework Assignment Page 322 #3-15 Page 323 #17-22, #25-27, 29-31,

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

Sect. 5.5 Inequalities in One Triangle Goal 1 Comparing Measurements of a Triangle. Goal 2 Using the Triangle Inequality.

Chapter 4-3 Inequalities in One Triangle Inequalities in Two Triangles.

5.4 Inequalities in One Triangle

Triangle Inequalities

The Triangle Inequality Thm. & Inequalities Involving 2 Triangles

5-5 Inequalities in Triangles

Inequalities in two triangles

6.5 Inequalities in Triangles and Indirect Proofs

Chapter 6 Inequalities in Geometry page 202

Inequalities in Two Triangles

Converse of Hinge Theorem

7-4 Triangle Inequality Theorem

3.7 Angle-Side Theorems Objective:

Triangle Inequalities

Inequalities in One Triangle

6.5 & 6.6 Inequalities in One and Two Triangle

6-4 Inequalities for One Triangle

Triangle Inequalities

Inequalities for One Triangle

6.5 & 6.6 Inequalities in One and Two Triangle

Try This… Measure (using your ruler), three segments 2 inches

TRIANGLE INEQUALITY THEOREM

5.5 Use Inequalities in a ∆ Mrs. vazquez Geometry.

Honors Geometry.

Triangle Inequalities

TRIANGLE INEQUALITY THEOREM

TRIANGLE INEQUALITY THEOREM

Triangle Inequalities

Lesson 6.7 Congruent Triangles pp

Side – Angle Inequalities

GEOMETRY The Triangle Inequality

Side – Angle Inequalities

Have your homework out when the bell rings.

List the angles and sides from smallest to largest

Triangle Inequalities

7-5: Inequalities in a Triangle

Triangle Inequalities

Section 5-5 Inequalities in triangles

Presentation transcript:

Lesson 7.4 Inequalities pp. 281-286

Objectives: 1. To state and prove the Longer Side Inequality. 2. To state and prove the Hinge Theorem.

Theorem 7.12 Longer Side Inequality. One side of a triangle is longer than another side if and only if the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side.

Which angle is the largest? Which angle is the smallest? X Y Z 7 5 4 Which angle is the largest? Which angle is the smallest?

Which side is the longest? Which side is the shortest? X Y Z 100° 20° 60° Which side is the longest? Which side is the shortest?

Practice: List the angles from smallest to largest. B C 6 3 5 Practice: List the angles from smallest to largest. 1. A,B,C 2. C,B,A 3. B,C,A 4. C,A,B

Practice: List the angles from smallest to largest. AB = 4, BC = 7, AC = 5 1. A, B, C 2. C, B, A 3. B, C, A 4. C, A, B

Theorem 7.13 Hinge Theorem. Two triangles have two pairs of congruent sides. If the measure of the included angle of the first triangle is larger than the measure of the other included angle, then the opposite (3rd) side of the first triangle is longer than the opposite side of the second triangle.

A B C If mA  mW, then CB  YX. W X Y

Homework pp. 283-286

►A. Exercises 1. Give the order of sides from smallest to largest. C A B 70° 65° 45°

►A. Exercises 3. Give the order of sides from smallest to largest. M N 66° 50° 64°

►A. Exercises 5. Give the order of angles from smallest to largest. F 14 15 27

►A. Exercises 7. Give the order of angles from smallest to largest. 4 3 5 X Y Z

►A. Exercises For each pair of triangles, compare an unlabeled pair of sides or angles. 9. U M F Y Z I 5 7 6 8

►A. Exercises For each pair of triangles, compare an unlabeled pair of sides or angles. 11. A B C 5 3 Q P R 3 5

Given: ∆ABC; B is right angle Prove: AC is the longest side ►A. Exercises Prove the following statement. 13. In a right triangle the hypotenuse is the longest side. Given: ∆ABC; B is right angle Prove: AC is the longest side A B C

►B. Exercises Prove the following statement. 14. The shortest segment from a point to a line is a perpendicular segment.

►B. Exercises 14. Given: AB  BC Prove: AC  AB A B C D E

■ Cumulative Review 21. mPBA if l || m Give an algebraic expression or a numerical value for each indicated angle. 21. mPBA if l || m P A B 37 l m

■ Cumulative Review 22. mA Give an algebraic expression or a numerical value for each indicated angle. 22. mA B A C D E

■ Cumulative Review 23. mABC Give an algebraic expression or a numerical value for each indicated angle. 23. mABC A B C x

■ Cumulative Review 24. mR Give an algebraic expression or a numerical value for each indicated angle. 24. mR Q R P x

■ Cumulative Review 25. mA Give an algebraic expression or a numerical value for each indicated angle. 25. mA B A C x 2x – 5