Inequalities in Triangles

Slides:

Advertisements

Similar presentations

5-3 Inequalities in One Triangle

Advertisements

The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

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.

TODAY IN GEOMETRY…  Learning Target: 5.5 You will find possible lengths for a triangle  Independent Practice  ALL HW due Today!

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

5.5 Inequalities in Triangles

Anna Chang T2. Angle-Side Relationships in Triangles The side that is opposite to the smallest angle will be always the shortest side and the side that.

5-2 Inequalities and Triangles

Triangle Inequalities

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!

5.5 Use Inequalities in a Triangle

5-6 Inequalities in One Triangle

Inequalities in One Triangle

L.E.Q. How do you use inequalities involving angles and sides of triangles?

Triangle Sum Properties & Inequalities in a Triangle Sections 4.1, 5.1, & 5.5.

5.5Use Inequalities in a Triangle Theorem 5.10: If one side of a triangle is longer than the other side, then the angle opposite the longest side is _______.

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

5.5 Inequalities in Triangles

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

Inequalities for Sides and Angles of a Triangle Section 5-3.

5-5 Triangle Inequalities. Comparing Measures of a Triangle There is a relationship between the positions of the longest and shortest sides of a triangle.

Triangle Inequalities What makes a triangle and what type of triangle.

GEOMETRY HELP Explain why m  4 > m  5. Substituting m  5 for m  2 in the inequality m  4 > m  2 produces the inequality m  4 > m  5.  4 is an.

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.

Chapter 4 Section 4.1 Section 4.2 Section 4.3. Section 4.1 Angle Sum Conjecture The sum of the interior angles of a triangle add to 180.

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

Thursday, November 8, 2012 Agenda: TISK & No MM Lesson 5-5: Triangle Inequalities Homework: 5-5 Worksheet.

Inequalities and Triangles

LESSON 5-5 INEQUALITIES IN TRIANGLES OBJECTIVE: To use inequalities involving angles and sides of triangles.

Geometry Section 5.5 Use Inequalities in a Triangle.

Chapter 5: Relationships Within Triangles 5.5 Inequalities in Triangles.

Triangle Inequality Theorem and Side Angle Relationship in Triangle

4.7 Triangle Inequalities

5.5 Inequalities in Triangles Learning Target I can use inequalities involving angles and sides in triangles.

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.

5-3 Inequalities in One Triangle 5-4 Indirect proof 5-5 The triangle Inequality 5-6 Inequality in two triangles. Chapter 5.

Triangle Inequalities Objectives: 1.Discover inequalities among sides and angles in triangles.

5-3 Inequalities and Triangles The student will be able to: 1. Recognize and apply properties of inequalities to the measures of the angles of a triangle.

Chapter 5 Lesson 5 Objective: To use inequalities involving angles and sides of triangles.

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

HONORS GEOMETRY 5.3. Inequalities in One Triangle.

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

Triangle Inequalities

January Vocab Quiz on Sections Bell Ringer

Chapter Inequalities in One Triangle 5-4 Indirect proof 5-5 The triangle Inequality 5-6 Inequality in two triangles.

5.2: Triangle Inequalities

5.5 Inequalities in One Triangle

Triangle Inequalities

Inequalities in One Triangle

6.5 & 6.6 Inequalities in One and Two Triangle

Inequalities and Triangles

5-2 Inequalities and Triangles

Triangle Inequalities

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

LESSON 5-5 INEQUALITIES IN TRIANGLES OBJECTIVE: To use inequalities involving angles and sides of triangles.

TRIANGLE INEQUALITY THEOREM

Triangle Theorems.

Class Greeting.

5.5 Inequalities in Triangles

Use Inequalities in a Triangle

TRIANGLE INEQUALITY THEOREM

TRIANGLE INEQUALITY THEOREM

Triangle Inequalities

INEQUALITIES Sides/Angles of Triangles

5-2 Inequalities and Triangles

Inequalities for Sides and Angles of a Triangle

List the angles and sides from smallest to largest

Triangle Inequalities

Presentation transcript:

Inequalities in Triangles

Definition of Inequality For any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c.

Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.

Examples Find all measures less than angle 7.

Examples Find all measures greater than angle 6.

Examples Find all measures greater than angle 1.

Examples Find all measures greater than angle 8.

Angle-Side Relationships If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

Examples List the angles of PQR in order from smallest to largest.

Examples List the angles of PQR in order from smallest to largest.

Angle-Side Relationships If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

Examples List the sides of FGH in order from shortest to longest.

Examples List the sides of WXY in order from shortest to longest.

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Examples Is it possible to form a triangle with the given side lengths? If not, explain why not. 8, 15, 17

Examples Is it possible to form a triangle with the given side lengths? If not, explain why not. 6, 8, 14

Examples Is it possible to form a triangle with the given side lengths? If not, explain why not. 15, 16, 30

Examples Is it possible to form a triangle with the given side lengths? If not, explain why not. 2, 8, 11

Triangle Inequality Theorem When the lengths of two sides of a triangle are known, the third side can be any length in a range of values. You can use the Triangle Inequality Theorem to determine the range of possible lengths for the third side.

Triangle Inequality Theorem To do this, find the sum and the difference of the two known sides. The sum provides the upper limit and the difference provides the lower limit. 13 + 9 = 22 13 – 9 = 4 4 < n < 22