Indirect Proof and Inequalities 5 5 in One

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Indirect Proof and Inequalities 5 -5 in One Triangle The positions of the longest

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 Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 1: Ordering Triangle Side

Indirect Proof and Inequalities 5 -5 in One Triangle Example 1: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest. The shortest side is smallest angle is F. , so the The angles from smallest to largest are F, H and G. Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 2: Ordering Triangle Side

Indirect Proof and Inequalities 5 -5 in One Triangle Example 2: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest. m R = 180° – (60° + 72°) = 48° The smallest angle is R, so the shortest side is. The sides from shortest to longest are Holt Geometry 48°

Indirect Proof and Inequalities 5 -5 in One Triangle Example 3: Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 3: Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 4: Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 4: Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle A triangle is formed by

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 Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle A certain relationship must exist

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. NOTE: Just check that the sum of the two shorter sides is greater than the longest side. Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 5: Applying the Triangle

Indirect Proof and Inequalities 5 -5 in One Triangle Example 5: Applying the Triangle Inequality Theorem Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 5: Applying the Triangle

Indirect Proof and Inequalities 5 -5 in One Triangle Example 5: Applying the Triangle Inequality Theorem Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 6: Finding Possible Side

Indirect Proof and Inequalities 5 -5 in One Triangle Example 6: Finding Possible 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. Let x represent the length of the third side. Then apply the Triangle Inequality Theorem. x + 8 > 13 x>5 8 + 13 > x 21 > x Combine the inequalities. So 5 < x < 21. The length of the third side is greater than 5 inches and less than 21 inches. Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Example 7 The lengths of

Indirect Proof and Inequalities 5 -5 in One Triangle Example 7 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 Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle You can also use side

Indirect Proof and Inequalities 5 -5 in One Triangle You can also use side lengths to classify a triangle as acute or obtuse. Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry

Indirect Proof and Inequalities 5 -5 in One Triangle Holt Geometry