5.5 Inequalities in Triangles

Slides:

Advertisements

Similar presentations

Example 6 = 2 + 4, with c = 4, then 6 > 2

Advertisements

Median ~ Hinge Theorem.

CHAPTER 6: Inequalities in Geometry

Use Inequalities in a Triangle Ch 5.5. What information can you find from knowing the angles of a triangle? And Vice Verca.

Inequalities in One Triangle

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.

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.

Chapter 5: Inequalities!

Lesson 4.3 – Triangle inequalities & Exterior Angles

Triangle Inequalities

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

Properties of Triangles

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!

Final Exam Key Concepts.

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

5.5 Use Inequalities in a Triangle

5-6 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.

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

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.

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.

Day 7 agenda Go over homework- 5 min Take up for an effort grade Warm-up- 10 min 5.5 notes- 50 min Start homework- 20 min Make sure students have time.

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.

Name the angles opposite of each side:  X is opposite of YZ  Y is opposite of XZ  Z is opposite of XY X Y Z.

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

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 –

5.5 Inequalities in Triangles DOM Can you figure out the puzzle below??? Domino.

Geometry Section 5.5 Use Inequalities in a Triangle.

5.5 Inequalities in Triangles DOM Can you figure out the puzzle below??? Domino.

Chapter 5: Relationships Within Triangles 5.5 Inequalities in Triangles.

4.7 Triangle Inequalities

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

5.5 Indirect Reasoning -Indirect Reasoning: All possibilities are considered and then all but one are proved false -Indirect proof: state an assumption.

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

 Students will be able to use inequalities involving angles and sides of triangles.

5.3 Trade Routes and Pasta Anyone?

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

Triangle Inequalities

5.1 Midsegments of Triangles

5-5 Inequalities in Triangles

Angles of Triangles.

January Vocab Quiz on Sections Bell Ringer

Review For Unit 2 – Quiz # 4 Triangle Inequality Theorem

Exterior Angles.

Inequalities in One Triangle

6.5 & 6.6 Inequalities in One and Two Triangle

Inequalities for One Triangle

Entry Task *Use the geosticks as models for the different board lengths. You will need 2 green, 2 orange, 1 brown, 1 blue and 1 lime green to represent.

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

5.5 Inequalities in Triangles

Inequalities in Geometry

Use Inequalities in a Triangle

TRIANGLE INEQUALITY THEOREM

TRIANGLE INEQUALITY THEOREM

Triangle Inequalities

Inequalities in Triangles

Triangle Inequalities

Section 5-5 Inequalities in triangles

Presentation transcript:

5.5 Inequalities in Triangles DOM Can you figure out the puzzle below??? Domino

Comparison Property of Inequality b c Comparison Property of Inequality: If a = b + c, and c > 0, then a > b.

Proof of Comparison Property of Inequality Given: a = b + c, c > 0 Prove: a > b Statements Reasons 1. 2. 3. 4. 5. c > 0 b + c > b + 0 b + c > b a = b + c a > b

Theorem Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles. Insert figure from home

Application Given the figure below, explain why . 1. 1. 2. 2. 3. 3. Statements Reasons 1. 2. 3. 1. 2. 3. 5

Theorem Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Insert figure from home 6

Example List the angles of the following figure in order from smallest to largest. 7

Theorem Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. Insert figure from home 8

Sides of a Triangle List the sides of the following triangle in order from shortest to longest. Determine which segment is shortest in the following diagram.

Theorem Theorem 5-12: Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Insert figure from home 10

Theorem Can a triangle have sides with the given lengths? a) 7 ft, 3 ft, 8 ft b) 10 cm, 6 cm, 3 cm A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side. 11

5.5 Inequalities in Triangles HW 5.5: #1-25 (1st column), 32, 33, 35 p.192: #3-4, 11, 22, 24-26 Scrambled Eggs

Midterm Review Given the figure below, name the type of angle pairs given.

Midterm Review Find . Justify each answer. 1) 2) 135° 1 2 14

Midterm Review Find x in the following polygon. x° 125° 125° 15

Midterm Review Find the equation of a line that goes through the point (-2, 1) and (3,2). Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5). 16