Side – Angle Inequalities

Slides:

Advertisements

Similar presentations

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

Advertisements

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

5-2 Inequalities and Triangles

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.

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 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!

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

Inequalities in One Triangle

Use Inequalities in A Triangle

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right 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

Course: Applied Geometry Aim: What is Triangle Inequality Theorem Aim: What is Triangle Inequality? Do Now: Sketch 9.

Chapter 5 Section 5.5 Inequalities in 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.

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.

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

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.

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.

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.

4.7 Triangle Inequalities

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.

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

Chapter 5 Lesson 5 Objective: To use inequalities involving angles and sides of triangles.

Side-side-side (SSS) postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

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

5-5 Inequalities in Triangles

7-4 Triangle Inequality Theorem

Triangle Inequalities

Triangle Inequalities

Triangle Inequality Theorem

You found the relationship between the angle measures of a triangle. Recognize and apply properties of inequalities to the measures of the angles.

5.5 Inequalities in One Triangle

Drawing Triangles.

Triangle Inequalities

4.5 - Isosceles and Equilateral Triangles

6-4 Inequalities for One Triangle

Triangle Inequalities

Triangle Inequalities

Inequalities for One Triangle

Triangle Inequality Theorem

Pythagorean Theorem a²+ b²=c².

Triangle Theorems.

5.5 Use Inequalities in a ∆ Mrs. vazquez Geometry.

7.3 Triangle Inequalities

Inequalities in One Triangle

Honors Geometry.

Use Inequalities in a Triangle

Triangle Inequalities

5-5 Triangle Inequality Theorem

The Triangle Inequality

Side – Angle Inequalities

Have your homework out when the bell rings.

Triangle Inequalities

Triangle Inequalities

Presentation transcript:

Side – Angle Inequalities 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 smaller side.

Ex. 1 Write the measurements of the angles in order from least to greatest. 52 12 B C 43 Step 1. Write the sides in order from least to greatest. AB, BC, AC Step 2. Write the angles opposite those sides. C, A, B

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. Ex. 2 Write the measurements of the sides in order from least to greatest. Step 1. List the angles in order from least to greatest. X, Z, Y Step 2. Write the sides opposite those angles. Y YZ, XY, XZ 128º X 22º 30º Z

Right Triangles hypotenuse leg leg hypotenuse In a right triangle, the ___________ is the side with the greatest measure.

7-4 Triangle Inequality Theorem The sum of the measure of any two sides of a triangle is greater than the third side. C AB + BC > AC AB + AC > BC BC + AC > AB B A

Ex. 1 Determine if the three numbers can be measures of the sides of a triangle. If no, explain. 13, 28, 19 9, 4, 4 c. 9, 7, 2 Yes, 13 + 19  28 13, 19, 28 NO, 4 + 4  9 4, 4, 9 NO, 7 + 2  9 2, 7, 9

Ex. 2 If two sides of a triangle have the following measures, find the range of possible measures of the third side. 10, 7 b. 18 , 11 18 + 11  x x + 11  18 10 + 7  x x + 7  10 29  x 17  x x  7 x < 29 x < 17 x  3 3 < x < 17 7 < x < 29