Lesson 5.5 Inequalities Involving Two Triangles. SAS Inequality TheoremSSS Inequality Theorem (Hinge Theorem) - When 2 sides of a triangle are congruent.

Slides:



Advertisements
Similar presentations
Lesson 5 – 6 Inequalities in Two Triangles
Advertisements

Triangle Inequality Theorem:
Chapter 5: Inequalities!
5-7 Inequalities in Two Triangles
5-6 Inequalities in Two Triangles
Triangle Inequalities
Math I Unit 3 Concept: Triangular Inequalities The Hinge Theorem.
The Hinge Theorem Sec 5.6 Goal: To use the hinge theorem.
5.7 Inequalities in Two Triangles
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.
5.6 Indirect Proof and Inequalities in Two triangles.
Honors Geometry Section 4.8 Triangle Inequalities
Lesson 3-2: Isosceles Triangle
Lesson 3-3: Triangle Inequalities 1 Lesson 3-3 Triangle Inequalities.
5-6 Inequalities in One Triangle
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.
 Earlier in this chapter, we looked at properties of individual triangles using inequalities.  We know that the largest angle is opposite the longest.
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.
5-5 Indirect Proof. Indirect Reasoning In indirect reasoning, all possibilities are considered and then all but one are proved false. – The remaining.
Triangle Sum Theorem The sum of the angle measures in a triangle is 180 degrees.
LEQ: How can use angle measures or side lengths to make conclusions in triangles?
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.
Isosceles and Equilateral Triangles
Answers to Homework 2. 2, n, 17n 6. 5, 2k  DF 12. OA 14. VB 16.  3 >  1 >  2.
5.7 Inequalities in Two Triangles
Triangle Inequalities. Triangle Inequality #1 Triangle Inequality 1(577031).ggb Triangle Inequality 1(577031).ggb This same relation applies to sides.
Warm-up 1) Write an inequality to describe the length of MN. (Look at the picture) 2) Find the range for the measure of the third side of a triangle if.
5.6 Notes Inequalities in One Triangle. Comparison Property of Inequality.
5.4 Inequalities in One Triangle
Triangle Inequalities
January Vocab Quiz on Sections Bell Ringer
Lesson 3-2: Isosceles Triangle
Angle Side Theorems Lesson 3.7.
Inequalities in two triangles
Inequalities in Two Triangles
Inequalities in Two Triangles
Inequalities for Two Triangles
Converse of Hinge Theorem
BASIC GEOMETRY Section 5.6: Inequalities in 2 Triangles
7-4 Triangle Inequality Theorem
Lesson 4.6 Isosceles Triangles.
Triangle Inequalities
Triangle Inequalities
6.5 & 6.6 Inequalities in One and Two Triangle
Warm-up Find x a) b).
Bellwork 1) AG = 18 cm. What is AD? 2) Solve for x.
5-6 Inequalities in Two Triangles
Triangle Inequalities
Inequalities in 2 triangles
6.5 & 6.6 Inequalities in One and Two Triangle
5-6 Hinge Theorem Rigor – Explore inequalities in 2 triangles
TRIANGLE INEQUALITY THEOREM
Base Angles & Exterior Angles
TRIANGLE INEQUALITY THEOREM
Lesson 7.4 Inequalities pp
TRIANGLE INEQUALITY THEOREM
Triangle Inequalities
Side – Angle Inequalities
Inequalities in Two Triangles
Side – Angle Inequalities
INEQUALITIES Sides/Angles of Triangles
Lesson 3-2 Isosceles Triangles.
Lesson 3-2 Isosceles Triangles.
Triangle Inequalities
Triangle Basics Lesson 2
Section 5-5 Inequalities in triangles
Inequalities in Two Triangles
Presentation transcript:

Lesson 5.5 Inequalities Involving Two Triangles

SAS Inequality TheoremSSS Inequality Theorem (Hinge Theorem) - When 2 sides of a triangle are congruent to 2 sides of another triangle, and the included angle of one triangle is greater than the included angle of the other triangle… Then, the side opposite the larger angle is larger than the side opposite the smaller angle - When 2 sides of a triangle are congruent to 2 sides of another triangle, and the 3 rd side of a triangle is greater than the 3 rd side of the other triangle… Then, the angle opposite the larger side is larger than the angle opposite the smaller side

A. Compare the measures AD and BD.

B. Compare the measures  ABD and  BDC.

ALGEBRA Find the range of possible values for a.

Find the range of possible values of n.