Use Inequalities in a Triangle Ch 5.5. What information can you find from knowing the angles of a triangle? And Vice Verca.

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Presentation transcript:

Use Inequalities in a Triangle Ch 5.5

What information can you find from knowing the angles of a triangle? And Vice Verca

What does this mean? The angle opposite the longest side is the largest angle. The angle opposite the shortest side is the smallest angle. VICE VERCA The side opposite the smallest angle is the shortest side. The side opposite the largest angle is the longest side.

Name the sides from smallest to largest 82 ô 58 ô 40 ô

Name the sides from smallest to largest 109 ô 52 ô 19 ô

Page 331 #6 - 15

Recall… That the sum of the two smaller sides of a triangle must be larger than the longest side. This theorem states that ANY two sides must be longer than the third side.

Can these sides make up a triangle? 3, 4, 5 1, 1, 2 2, 3, 4 8, 11, 15

What is a possible third side length? There are two possible situations that can occur: 1. You have the two smallest sides, so the third side has to be smaller than their sum. 2. You have the one side and the largest side, so the smaller number plus some number must be bigger than the larger number.

Example Describe the possible lengths of the third side of the triangle given the lengths of the other two sides: 6 ft, 13 ft Situation 1 (2 smaller sides): side + side > missing side > x 19>x, so x < 19 Situation 2 (Largest and other side): side + x > largest side 6 + x > 13 x > 7

Another Example Describe the possible lengths of the third side of the triangle given the lengths of the other two sides: 3 in, 21 in

Example with diagram 357

Make it more difficult!

One more for good luck… 3x - 1 2x + 1 x + 5

Page 331 #16 – 21, 33, 34