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

Slides:

Advertisements

Similar presentations

Warm-up: Solve for x and classify the triangle. (5x + 2) (6x + 5) (4x + 8) (9x + 7) (4x + 8) (9 – x)

Advertisements

5-3 Inequalities in One Triangle

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

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.

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

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

Draw the following: 1. acute triangle 2.right triangle 3.obtuse triangle 4. acute, scalene triangle 5.obtuse, isosceles triangle 6. right, scalene.

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

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.

Triangle Inequalities

Honors Geometry Section 4.8 Triangle Inequalities

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!

5.5 Use Inequalities in a Triangle

Lesson 3-3: Triangle Inequalities 1 Lesson 3-3 Triangle Inequalities.

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.

5-6 Inequalities in One Triangle

Use Inequalities in A Triangle

3.3 Triangle Inequality Conjecture. How long does each side of the drawbridge need to be so that the bridge spans the river when both sides come down?

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 _______.

Triangle Inequalities

6.4 Triangle Inequalities. Angle and Side Inequalities  Sketch a good size triangle in your notebook (about a third of the page).  Using a ruler find.

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.

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.

LEQ: How can use angle measures or side lengths to make conclusions in triangles?

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.

1 Triangle Inequalities. 2 Triangle Inequality The smallest side is across from the smallest angle. The largest angle is across from the largest side.

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.

Geometry Section 5.5 Use Inequalities in a Triangle.

Triangle Inequality Theorem and Side Angle Relationship in Triangle

4.7 Triangle Inequalities

Triangle Inequalities. Triangle Inequality #1 Triangle Inequality 1(577031).ggb Triangle Inequality 1(577031).ggb This same relation applies to sides.

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.

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

Chapter 5.5 Notes: Use Inequalities in a Triangle Goal: You will find possible side lengths of a triangle.

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

5.4 Inequalities in One Triangle

Triangle Inequalities

Homework: Maintenance Sheet 17 *Due Thursday

Triangle Inequalities

Follow the directions and complete both sides of the activity

EOC Prep: Triangles.

Homework: Maintenance Sheet 17 *Due Thursday

Triangle Inequalities

Bellwork 1) AG = 18 cm. What is AD? 2) Solve for x.

Triangle Inequalities

Triangle Inequalities

Inequalities for One Triangle

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

TRIANGLE INEQUALITY THEOREM

Use Inequalities in a Triangle

Triangle Inequalities

TRIANGLE INEQUALITY THEOREM

TRIANGLE INEQUALITY THEOREM

Triangle Inequalities

Inequalities in Triangles

Have your homework out when the bell rings.

List the angles and sides from smallest to largest

Triangle Inequalities

Triangle Inequalities

Section 5-5 Inequalities in triangles

Presentation transcript:

Try This… Measure (using your ruler), three segments 2 inches Using those segment lengths, draw a triangle.

Triangle Inequality Conjecture Conjecture: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Are These Triangles Possible? 5, 8, 15 6, 10, 20 7, 8, 17 10, 12, 20 If two sides of a triangle are 6 and 10, the missing angle must be between what two measures?

Side-Angle Inequality Conjecture Conjecture: In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

In other words… The largest angle is across from the longest side. The smallest angle is across from the shortest side. The medium angle is across from the mid-sized side.