Section 4.3: Triangle Inequalities
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. To find a range of values for the third side when given two lengths, write two inequalities: one inequality that assumes the larger value given is the longest side in the triangle and one inequality that assumes that the third side is the longest side in the triangle. Combine the two inequalities for the final answer.
In any triangle, the largest angle is opposite the largest side (the opposite side of an angle is the side that does not form the angle). The shortest angle is opposite the shortest side. Therefore, the angle measures can be used to list the size order of the sides. The converse is also true: the lengths of the sides can be used to order the relative size of the angles.Triangle side and angle inequalities are important when solving proofs.
If one side of a triangle is extended beyond the vertex, an exterior angle is formed. This exterior angle is supplementary with its adjacent, linear angle. Since the angle sum in a triangle is also 180 degrees, the exterior angle must have a measure equal to the sum of the remaining angles, called the remote interior angles.
In any triangle, the largest angle is opposite the largest side (the opposite side of an angle is the side that does not form the angle). The shortest angle is opposite the shortest side. Therefore, the angle measures can be used to list the size order of the sides. The converse is also true: the lengths of the sides can be used to order the relative size of the angles.Triangle side and angle inequalities are important when solving proofs.
If one side of a triangle is extended beyond the vertex, an exterior angle is formed. This exterior angle is supplementary with its adjacent, linear angle. Since the angle sum in a triangle is also 180 degrees, the exterior angle must have a measure equal to the sum of the remaining angles, called the remote interior angles.
Notes and Powerpoints
lesson_4.3.pdf | |
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sketchpad4-3.gsp | |
File Size: | 58 kb |
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exterior4.3.gsp | |
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Homework/Classwork
Interactive Triangle Inequality
Interactive Self Quiz
formingtrianglesactivity.pdf | |
File Size: | 69 kb |
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Puzzle:
Given a rope with knots tied at equal intervals, form a triangle with the rope such that each vertex of the triangle occurs at a knot.
Suppose the rope has 13 knots, dividing the rope into 12 sections of equal length, with a perimeter of 12 units.
Let the sides of the triangle be x, y, and z. Make a table of all values of x, y, and z that satisfy the conditions of a perimeter of 12 units and the Triangle Inequality Theorem.
Suppose the rope has 13 knots, dividing the rope into 12 sections of equal length, with a perimeter of 12 units.
Let the sides of the triangle be x, y, and z. Make a table of all values of x, y, and z that satisfy the conditions of a perimeter of 12 units and the Triangle Inequality Theorem.