7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures...

7
7-4: Triangle Inequality Theorem

Transcript of 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures...

Page 1: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

Page 2: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the measure of the third side.

We use the Triangle Inequality Theorem to determine if three sides can form a triangle.

Page 3: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

Determine if the three numbers can be measures of the sides of a triangle. 5, 7, 4

5 + 7 > 4 true 5 + 4 > 7 true 7 + 4 > 5 true Since all cases are true, these measures can form a triangle.

11, 3, 7 11 + 3 > 7 true 11 + 7 > 3 true 3 + 7 > 11 false Since there is at least one false statement, these measures

cannot form a triangle.

Page 4: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

YOUR TURN Determine if 16, 10, and 5 can be the measures of the

sides of a triangle. If not, explain. No, 5 + 10 is not greater than 16

Page 5: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

If you are given two sides to a triangle, then the unknown side must be: Less than the sum of the known sides, and Greater than the difference of the known sides

Example If two sides of a triangle are 17 and 8, find the range of

possible measures for the third side. 17 + 8 = 25 17 – 8 = 9 The third side must be 9 < x < 25

Page 6: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

YOUR TURN If two sides of a triangle are 9 and 13, find the range of

possible measures for the third side. 4 < x < 22

Page 7: 7-4: Triangle Inequality Theorem. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the.

7-4: Triangle Inequality Theorem

Assignment Worksheet #7-4

Tomorrow Quiz on 7-1 through 7-3

Monday Distribution of chapter 7 preview

Wednesday Chapter 7 test


Unit 4: Right Triangles Triangle Inequality Pythagorean Theorem and its Converse Trigonometry Inverse Trigonometry Solving Right Triangles.

Unit 4: Right Triangles Triangle Inequality Pythagorean Theorem and its Converse Trigonometry Inverse Trigonometry Solving Right Triangles.

Apply inequalities in one triangle. Objectives. Triangle inequality theorem Vocabulary.

Apply inequalities in one triangle. Objectives. Triangle inequality theorem Vocabulary.

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem.

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem.

Splash Screen. Lesson 4 Menu Five-Minute Check (over Lesson 5-3) Main Ideas California Standards Theorem 5.11: Triangle Inequality Theorem Example 1:

Splash Screen. Lesson 4 Menu Five-Minute Check (over Lesson 5-3) Main Ideas California Standards Theorem 5.11: Triangle Inequality Theorem Example 1:

Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Mathematical Practices - Ledyard · 2016. 3. 10. · Pythagorean Theorem to solve right triangles in applied problems (Triangle inequality theorem) CC.9-12.G.SRT.8 Use trigonometric

Mathematical Practices - Ledyard · 2016. 3. 10. · Pythagorean Theorem to solve right triangles in applied problems (Triangle inequality theorem) CC.9-12.G.SRT.8 Use trigonometric

Triangle Inequalities. Triangle Inequality #1 Triangle Inequality 1(577031).ggb Triangle Inequality 1(577031).ggb This same relation applies to sides.

Triangle Inequalities. Triangle Inequality #1 Triangle Inequality 1(577031).ggb Triangle Inequality 1(577031).ggb This same relation applies to sides.

TRIANGLE INEQUALITY THEOREM

TRIANGLE INEQUALITY THEOREM

The Triangle Midsegment Theorem

The Triangle Midsegment Theorem

Unit 2 MM1G3 b Triangle Inequality, Side-Angle Inequality and Exterior Angle Inequality.

Unit 2 MM1G3 b Triangle Inequality, Side-Angle Inequality and Exterior Angle Inequality.

MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem. Which of the following statements.

MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem. Which of the following statements.

Triangle Midsegment Theorem

Triangle Midsegment Theorem

Triangle Inequality Theorem - Westhampton Beach ... sides of an isosceles triangle are 4 and 8. What is the third side? A) 8 B) 5 C) 4 D) 6 4. Two sides of an isosceles triangle are

Triangle Inequality Theorem - Westhampton Beach ... sides of an isosceles triangle are 4 and 8. What is the third side? A) 8 B) 5 C) 4 D) 6 4. Two sides of an isosceles triangle are

Station 1 Answer Key Triangle Inequality Theorem · Station 3 Case of the Missing Diagram 1) Easy: If the altitude of a triangle also bisects an angle of a triangle, then the triangle

Station 1 Answer Key Triangle Inequality Theorem · Station 3 Case of the Missing Diagram 1) Easy: If the altitude of a triangle also bisects an angle of a triangle, then the triangle

Triangle AngleSum Theorem1 Jul 24 9:36 AM 3.4 Triangle Angle Theorems I CAN... Apply the Triangle Angle Sum Theorem and Exterior Angle Theorem Jul 24 9:36 AM Triangle Angle Sum Theorem

Triangle AngleSum Theorem1 Jul 24 9:36 AM 3.4 Triangle Angle Theorems I CAN... Apply the Triangle Angle Sum Theorem and Exterior Angle Theorem Jul 24 9:36 AM Triangle Angle Sum Theorem

Properties of Triangles Unit 6. 5.5 Inequalities in One Triangle State Standards for Geometry 6. Know and use the Triangle Inequality Theorem. 13. Prove.

Properties of Triangles Unit 6. 5.5 Inequalities in One Triangle State Standards for Geometry 6. Know and use the Triangle Inequality Theorem. 13. Prove.

c 2007 The Author Topics in Inequalities – Theorems … Olympiad Training Materials/TIN, , ultrametric.googlepages.com Theorem 1.5. (Hadwiger-Finsler inequality) For any triangle

c 2007 The Author Topics in Inequalities – Theorems … Olympiad Training Materials/TIN, , ultrametric.googlepages.com Theorem 1.5. (Hadwiger-Finsler inequality) For any triangle

Triangles - Skyhawks Math! · Triangle Inequality Theorem..... 527 Triangles are interesting shapes. The triangle is a shape you'll often see in bridges and other buildings that need

Triangles - Skyhawks Math! · Triangle Inequality Theorem..... 527 Triangles are interesting shapes. The triangle is a shape you'll often see in bridges and other buildings that need

Indiana Academic Standards Geometry Crosswalk · inequality, inequality in one triangle, and the hinge theorem and its converse. G.T.6: Prove and apply the inequality theorems, including

Indiana Academic Standards Geometry Crosswalk · inequality, inequality in one triangle, and the hinge theorem and its converse. G.T.6: Prove and apply the inequality theorems, including

Triangle inequality (sides)

Triangle inequality (sides)