Triangle Inequalities

Slides:

Advertisements

Similar presentations

Median ~ Hinge Theorem.

Advertisements

Triangle Inequality Theorem:

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.

Chapter 5: Inequalities!

5-7 Inequalities in Two Triangles

Math I Unit 3 Concept: Triangular Inequalities The Hinge Theorem.

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

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.

Jeopardy Triangle Sides Triangle Inequality Hinge Theorem Converse of Hinge Theorem Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500.

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!

5.5 Use Inequalities in a Triangle

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

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.

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.

Chapter 6 Review. + DEFINITION OF INEQUALITY Difference in size, degree or congruence A B

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.

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.

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

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 –

Geometry Section 5.5 Use Inequalities in a Triangle.

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.

Chapter 5, Section 1 Perpendiculars & Bisectors. Perpendicular Bisector A segment, ray, line or plane which is perpendicular to a segment at it’s midpoint.

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

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

Triangle Inequalities

January Vocab Quiz on Sections Bell Ringer

Inequalities in two triangles

5.2: Triangle Inequalities

Inequalities in Two Triangles

Triangle Inequalities

5.5 Inequalities in One Triangle

Triangle Inequalities

6.5 & 6.6 Inequalities in One and Two Triangle

5-6 Inequalities in Two Triangles

Triangle Inequalities

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

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 in 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

Triangle Inequalities

Presentation transcript:

Triangle Inequalities Part 2

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

Example

Triangle Sides 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 from largest to smallest

Triangle Angles 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 triangle from largest to smallest

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Always check using the two smallest sides, they must be larger than the third. If this is true the numbers will represent a triangle.

Example Do these numbers represent a triangle? 1.) 9, 7, 12 Yes 2.) 5, 5, 10 No 3.) 1, 4, 6 4.) 6, 6, 2

Finding Range of Third Side If you are given two sides of a traingle you can determine the range that the third side must fall in. To find the smallest possible side length you subtract the larger side from the smaller side. The value you get can not be a side, however everything larger will work To find the largest your third side could be you add your two given sides, although this value will not work everything less than it will.

Example If you have two sides of a triangle 4 in and 7 in what is the range for the possible third side, n. 3in < n < 11in If you have two sides of a triangle 8 in and 12 in what is the range for the possible third side, n. 4in < n < 20in

Hinge Theorem If two sides of one triangle are congruent two two sides of another triangle, and the included angles are not congruent, then the longest side is opposite the larger included angle.

Example

Converse of the Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side.

Example