Inequalities in One Triangle

Slides:

Advertisements

Similar presentations

5.5 Inequalities in One Triangle

Advertisements

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

MM1G3b -Understand and use the triangle inequality, the side-angle inequality, and the exterior angle inequality.

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

5-2 Inequalities and Triangles

Chapter 5: Inequalities!

Triangle Inequalities

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.

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

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!

HOW TO FIND AN ANGLE MEASURE FOR A TRIANGLE WITH AN EXTENDED SIDE

5.5 Inequalities in One Triangle. Objectives: Students will analyze triangle measurements to decide which side is longest & which angle is largest; students.

5.5 Use Inequalities in a Triangle

5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your.

5-6 Inequalities in One Triangle

Use Inequalities in A Triangle

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.

Chapter 5 Section 5.5 Inequalities in a triangle.

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 Inequality Objective: –Students make conjectures about the measures of opposite sides and angles of triangles.

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.

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.

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

Objective: 5.3 & Inequalities in One/Two Triangle(s) _________& The Triangle Inequality Warm Up: Solve the inequality: 1. x + 3 < > 10.

1 Objectives State the inequalities that relate angles and lengths of sides in a triangle State the possible lengths of three sides of a triangle.

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 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your.

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.

Honors Geometry Section 4.8 cont. Triangle Inequality Proofs.

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

Inequalities in One Triangle Geometry. Objectives: Use triangle measurements to decide which side is longest or which angle is largest. Use the Triangle.

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.

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

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

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

5.4 Inequalities in One Triangle

7-4 Triangle Inequality Theorem

Notecards Unit 4 Triangle Properties.

Triangle Inequality Theorem

5.5 Inequalities in One Triangle

Inequalities in One Triangle

6.5 & 6.6 Inequalities in One and Two Triangle

Triangle Inequalities

Inequalities for One Triangle

Triangle Inequality Theorem

Triangle Theorems.

5.5 Use Inequalities in a ∆ Mrs. vazquez Geometry.

Inequalities in One Triangle

DRILL 4 Question Quiz will be collected and graded

Use Inequalities in a Triangle

Base Angles & Exterior Angles

5-5 Triangle Inequality Theorem

Side – Angle Inequalities

The Triangle Inequality

Inequalities in Triangles

Side – Angle Inequalities

INEQUALITIES Sides/Angles of Triangles

5-2 Inequalities and Triangles

T H E O R M S TRIANGLES CONCEPT MAP Prove Triangles are Congruent

Inequalities for Sides and Angles of a Triangle

Presentation transcript:

Inequalities in One Triangle Section 5.5 Inequalities in One Triangle

Theorem 5.10 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. 15 B 12 A

THEOREM 5.11 If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle 60 o Side 2 Side 1 > Side 2 45 o Side 1

Write the sides/angles in order from least to greatest. 15 33 63 C 32 B F 22 D

Is PQ>8? Is RQ<8? Q 57 61 P R 8

Exterior Angle Inequality The measure of an exterior angle of a triangle is greater then the measure of either of the two nonadjacent interior angles. A 1 B <1 is greater than <A <1 is greater than <B

What are the possible angle measures of <A? 42 A

Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A AB + BC >AC AC + BC > AB AB + AC > BC C B

Is it possible to have a triangle with the given side lengths? 3, 8, 3 6, 7, 12 9, 5, 11 8, 12, 20

What are the possible lengths of the third side of the triangle? 8, 17, ? 12, 18, ?

Write and solve the inequality PQ + QR > PR. 2x+1 3x-3 P R 3x+1