5 5 Use Inequalities in a Triangle Theorem

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5. 5 Use Inequalities in a Triangle Theorem 5. 10: If one side of

5. 5 Use 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 A is _______ than the angle opposite the shorter side. B 8 5 C

5. 5 Use Inequalities in a Triangle Theorem 5. 11: If one angle of

5. 5 Use Inequalities in a Triangle Theorem 5. 11: If one angle of a triangle is larger than another angle, then the side opposite the larger angle A is _______ than the side opposite the smaller angle. B 50 o 30 o C

5. 5 Use Inequalities in a Triangle Example 1 Write measurements in order from

5. 5 Use Inequalities in a Triangle Example 1 Write measurements in order from least to greatest Write measurements of the triangle in order from least to greatest. a. C b. 36 o B 57 o 87 o A Solution D E 22 12 13 F

5. 5 Use Inequalities in a Triangle Example 1 Write measurements in order from

5. 5 Use Inequalities in a Triangle Example 1 Write measurements in order from least to greatest Write measurements of the triangle in order from least to greatest. a. C b. 36 o B 57 o 87 o A Solution D E 22 12 13 F

5. 5 Use Inequalities in a Triangle Checkpoint. Write the measurements of the triangle

5. 5 Use Inequalities in a Triangle Checkpoint. Write the measurements of the triangle in order from least to greatest. B 99 o 1. A 34 o 47 o C

5. 5 Use Inequalities in a Triangle Checkpoint. Write the measurements of the triangle

5. 5 Use Inequalities in a Triangle Checkpoint. Write the measurements of the triangle in order from least to greatest. Q 2. P 80 o 45 o 55 o R

5. 5 Use Inequalities in a Triangle Theorem 5. 12: Triangle Inequality Theorem The

5. 5 Use Inequalities in a Triangle Theorem 5. 12: Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is A greater than the length of the third side. B C

5. 5 Use Inequalities in a Triangle Example 2 Find possible side lengths A

5. 5 Use Inequalities in a Triangle Example 2 Find possible side lengths A triangle has one side of length 14 and another of length 10. Describe the possible lengths of the third side. Solution Let x represent the length of the third side. Draw diagrams to help visualize the small and large values of x. Then use the Triangle Inequality Theorem to write and solve inequalities. Small values of x Large values of x The length of the third side must be greater than 4 and less than 24 ________________.

5. 5 Use Inequalities in a Triangle Checkpoint. Complete the following exercise 3. A

5. 5 Use Inequalities in a Triangle Checkpoint. Complete the following exercise 3. A triangle has one side 23 meters and another of 17 meters. Describe the possible lengths of the third side. Small values of x Large values of x The length of the third side must be greater than 6 meters or less than 40 meters

5. 5 Use Inequalities in a Triangle Theorem 5. 13: Exterior Angle Inequality Theorem

5. 5 Use Inequalities in a Triangle Theorem 5. 13: Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent interior angles.

5. 5 Use Inequalities in a Triangle Example 3 Relate exterior and interior angles

5. 5 Use Inequalities in a Triangle Example 3 Relate exterior and interior angles Solution So, by the Exterior Angle Inequality Theorem, _____ > 70 o and ______>_____.

5. 5 Use Inequalities in a Triangle Checkpoint. Complete the following exercise

5. 5 Use Inequalities in a Triangle Checkpoint. Complete the following exercise

5. 5 Use Inequalities in a Triangle Pg. 299, 5. 5 #1 -23

5. 5 Use Inequalities in a Triangle Pg. 299, 5. 5 #1 -23

Inequalities in One Triangle Geometry Objectives Use triangleInequalities in One Triangle Geometry Objectives Use triangle
TRIANGLE Segitiga Triangle Around Us Definition of triangleTRIANGLE Segitiga Triangle Around Us Definition of triangle
UROGENITAL TRIANGLE Urogenital triangle The urogenital triangle makesUROGENITAL TRIANGLE Urogenital triangle The urogenital triangle makes
Triangle Inequalities 1 Triangle Inequality l The smallestTriangle Inequalities 1 Triangle Inequality l The smallest
Lesson 3 3 Triangle Inequalities 1 Triangle InequalityLesson 3 3 Triangle Inequalities 1 Triangle Inequality
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
Triangle Sum Theorem Exterior Angle Theorem Work inTriangle Sum Theorem Exterior Angle Theorem Work in
Triangle Sum Theorem Exterior Angle Theorem Work inTriangle Sum Theorem Exterior Angle Theorem Work in
Special Right Triangles Theorem 4590 Triangle Theorem InSpecial Right Triangles Theorem 4590 Triangle Theorem In
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5