Triangle Inequalities

Slides:

Advertisements

Similar presentations

Triangle Inequalities

Advertisements

5.5 INEQUALITIES IN TRIANGLES (PART TWO). Think back…. What do we remember about the exterior angles of a 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.

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

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.

Chapter 5 Review Perpendicular Bisector, Angle Bisector, Median, Altitude, Exterior Angles and Inequality.

5.5 Use Inequalities in a Triangle

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

5-6 Inequalities in One Triangle

Use Inequalities in A Triangle

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

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

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

Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

Topic 5-7 Inequalities in one triangle. How many different triangles can we make using these six pieces? 2 1.What are your guesses? 2.What guess is too.

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

5-4 The Triangle Inequality. Triangle Inequality Theorem: The sum of two lengths in a triangle is always greater than the third length. Aulisio cut to.

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

Geometry Section 5.5 Use Inequalities in a Triangle.

4.7 Triangle Inequalities

5.4 The Triangle Inequality What you’ll learn: 1.To apply the triangle inequality Theorem 2.To determine the shortest distance between a point and a line.

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

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

5.4 Inequalities in One Triangle

Triangle Inequalities

Chapter 6 Inequalities in Geometry page 202

Triangle Inequalities

Homework: Maintenance Sheet 17 *Due Thursday

Triangle Inequalities

Homework: Maintenance Sheet 17 *Due Thursday

Triangle Inequalities

Lesson 5-4 The Triangle Inequality

Inequalities in One Triangle

6.5 & 6.6 Inequalities in One and Two Triangle

6-4 Inequalities for One Triangle

Triangle Inequalities

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

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

TRIANGLE INEQUALITY THEOREM

5.5 Inequalities in Triangles

5.5 Use Inequalities in a ∆ Mrs. vazquez Geometry.

Use Inequalities in a Triangle

Triangle Inequalities

TRIANGLE INEQUALITY THEOREM

TRIANGLE INEQUALITY THEOREM

Triangle Inequalities

The Triangle Inequality

Inequalities in Triangles

Homework Due Friday- goformative.com

Homework Due Friday- Maintenance Sheet 6.19 Goformative.com

5-4 Triangle Inequality Theorem

Triangle Inequalities

Unit Rate: a comparison of two measurements in which

Section 5-5 Inequalities in triangles

Presentation transcript:

Triangle Inequalities Modified by Lisa Palen

Triangle Inequality Theorem: Can you make a triangle? Yes!

Triangle Inequality Theorem: Can you make a triangle? NO because 4 + 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. a + b > c a + c > b b + c > a

Finding the range of the third side: Example Given a triangle with sides of length 3 and 7, find the range of possible values for the third side. Solution Let x be the length of the third side of the triangle. The maximum value: x < 3 + 7 = 10 The minimum value: x > 7 – 3 = 4 So 4 < x < 10 (x is between 4 and 10.) x < 10 x x > 4 x

Finding the range of the third side: Given The lengths of two sides of a triangle Since the third side cannot be larger than the other two added together, we find the maximum value by adding the two sides. Since the third side and the smallest side given cannot be larger than the other side, we find the minimum value by subtracting the two sides. Difference < Third Side < Sum

Finding the range of the third side: Example Given a triangle with sides of length a and b, find the range of possible values for the third side. Solution Let x be the length of the third side of the triangle. The maximum value: x < a + b The minimum value: x > |a – b| So |a – b|< x < a + b (x is between |a – b| and a + b.) x < a + b x > |a – b|

In a Triangle: The smallest angle is opposite the smallest side. The largest angle is opposite the largest side. The smallest side is opposite the smallest angle. The largest side is opposite the largest angle.

Theorem If one angle of a triangle is larger than a second angle, then the side opposite the first angle is larger than the side opposite the second angle. smaller angle larger angle longer side shorter side A B C

Theorem If one side of a triangle is larger than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Corollary #1: The perpendicular segment from a point to a line is the shortest segment from the point to the line. This side is longer because it is opposite the largest angle! This is the shortest segment!

Corollary #2: The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. This side is longer because it is opposite the largest angle! This is the shortest segment!