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Transcript
Indirect Proof and Inequalities 5-5 in One Triangle Objectives Apply inequalities in one triangle. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Example 1A: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Example 1B: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Check It Out! Example 2a Write the angles in order from smallest to largest. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Check It Out! Example 2b Write the sides in order from shortest to longest. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle A triangle is formed by three segments, but not every set of three segments can form a triangle. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle A certain relationship must exist among the lengths of three segments in order for them to form a triangle. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Example 3A: Applying the Triangle Inequality Theorem Tell whether a triangle can have sides with the given lengths. Explain. 7, 10, 19 Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Example 3B: Applying the Triangle Inequality Theorem Tell whether a triangle can have sides with the given lengths. Explain. 2.3, 3.1, 4.6 Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Example 4a: Finding Side Lengths The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third side. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Check It Out! Example 4b The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the third side. Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Example 5a: Travel Application The figure shows the approximate distances between cities in California. What is the range of distances from San Francisco to Oakland? Holt McDougal Geometry Indirect Proof and Inequalities 5-5 in One Triangle Check It Out! Example 5b The distance from San Marcos to Johnson City is 50 miles, and the distance from Seguin to San Marcos is 22 miles. What is the range of distances from Seguin to Johnson City? Holt McDougal Geometry
