1. MM1G3b -Understand and use the triangle inequality, the side-angle inequality, and the exterior angle inequality.

2. Important Triangle Facts  A triangle has 6 parts: 3 sides 3 angles  The sum of the angles in a triangle is always 180°.  A triangle is named by its vertices. A B C R T S Name the triangle and its parts. ∆ ABC ACBCAB < ACB < CBA < BAC ∆ RST RTSTRS < RST < STR < TRS

3.  Classify triangles by the side lengths. Equilateral Isosceles Scalene  Classify triangles by angle measures. Right Acute Obtuse Equiangular Do Parts I and II of the Triangle Notes Handout. Classifying Triangles – all sides are equal – no sides are equal – at least two sides are equal – has one 90 ⁰ angle – all angles are less than 90 ⁰ – has one angle greater than 90 ⁰ – all angles are equal

4. Triangle Side Angle Inequalities  Smaller angles are opposite shorter sides.  Larger angles are opposite longer sides. Example. 98 ⁰ 47 ⁰ 35 ⁰ 1. In ∆ABC, list the sides in order from smallest to largest. 2. In ∆JKL, list the angles in order from smallest to largest. 11 in 15 in 24 in AB, BC, AC < JLK, < KJL, < JKL

5.  Handout straight edges and compasses  Construct triangles: 3”, 4”, 5” 2”, 3”, 6”

6. Triangle Inequality Theorem  The sum of any two lengths of any two sides of a triangle is greater than the length of the third side. Could say that the sum of the two shorter sides must be greater than the longest side. If the 3 rd side is equal to or less than the sum of the 2 other sides, then it can not form a triangle. Examples – Can these three sides form a triangle? A. 5, 8, 16 B. 6, 11, 14 C. 8, 13, 5 5 + 816<NO 6 + 1114>YES 5 + 813=NO

7. Triangle Inequality Theorem  If two sides of a triangle are given, describe the possible lengths of the third side. A. 2 yd, 6 yd What possible values would work? Compare the sum of 2 shorter sides to longest side. So the third side has to be bigger than 4 and less than 8 or 4 < x < 8. If 3 rd side is 1: 1 + 2 > 6 If 3 rd side is 2: 2 + 2 > 6 If 3 rd side is 3: 3 + 2 > 6 If 3 rd side is 4: 4 + 2 > 6 If 3 rd side is 5: 5 + 2 > 6 If 3 rd side is 6: 6 + 2 > 6 If 3 rd side is 7: 6 + 2 > 7 If 3 rd side is 8: 6 + 2 > 8 If 3 rd side is 9: 6 + 2 > 9 If 3 rd side is 10: 6 + 2 > 10 No Yes No

8. Triangle Inequality Theorem  If two sides of a triangle are given, describe the possible lengths of the third side. A. 2 yd, 6 yd So the third side has to be bigger than 4 and less than 8 or 4 < x < 8. In other words, 2 + x > 6 or2 + 6 > x – 2 – 2 x > 4 or Therefore, the range is going to be x has to greater than the difference or less than the sum of the two given sides. 8 > x x < 8

9. Triangle Inequality Theorem  If two sides of a triangle are given, describe the possible lengths of the third side. B. 4 in, 12 in 4 + x > 12 and 4 + 12 > x – 4 x > 8 and 16 > x x < 16 21 > x x < 21 x < 15 C. 3 ft, 18 ft 3 + x > 18 and 3 + 18 > x – 3 – 3 8 < x < 16 15 < x < 21

10. Exterior Angle Inequality Theorem  The measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent (remote) interior angles.  The measure of an exterior angle is the sum of the remote interior angles. Example 1 2 34 53  65° 3(3x – 5)° 6 5 What do you know about x? What relationships do we know about the angles listed? < 2 <1 3x – 5 > 53 < 5 = < 2 + < 3 < 4 = <1 + <2 < 6 = <1 + < 3 < 3 <2 < 3 3x – 5 > 65 3x – 5 = 53 + 65 3x – 5 = 118 + 5 = +5 3x = 123 x = 41

11. Classwork/Homework  Textbook p287 (4-9,13-24 all)