Entry Task *Use the geosticks as models for the different board lengths. You will need 2 green, 2 orange, 1 brown, 1 blue and 1 lime green to represent the lengths given above. Green = 8 ft Orange = 5 ft Brown = 15 ft Blue = 12 ft Lime Green = 2 ft

Inequalities in One Triangle Section 5-6

Learning Targets I will be able to: Use inequalities involving sides and angles of triangles to solve problems.

Based on your observations from the entry task, what must be true about the lengths of the sides of any triangle? Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is ________ the length of the third side. greater than

Another way to think of it… What is the shortest path from home to school? School Daily Grind Home

Examples #1: Is it possible to draw a triangle with sides of 2 cm, 3 cm, and 5 cm? No, because 2 + 3 = 5, which is not greater than the third side.

#2: If 23 cm and 14 cm are the lengths of two sides of a triangle, what is the range of possible values for the length of the third side? Between 9 cm and 37 cm. (9 cm ‹ length ‹ 37 cm.)

Investigation #2: Comparing Sides and Angles Draw a large scalene triangle. It can be acute, obtuse, or even a right triangle. Measure the sides of the triangle as your draw it to make sure it is scalene. Measure the angles of your triangle with a protractor.

Label the vertex with the largest angle measure L, the vertex with the next largest measure M, and the vertex with the smallest measure S (for large, middle, and small). What is the relationship between the largest angle and the longest side? What about the smallest angle and shortest side? Does this seem to be true for all triangles?

Side-Angle Inequality Theorem: In a triangle, if two sides of a triangle are not congruent, then the larger angle is ________________ and the smaller angle is ________________. In our textbook this theorem is not named and it is split into two theorems. opposite the longer side opposite the shorter side

In other words… the longest side of a triangle is across from the largest angle; the shortest side of the triangle is across from the smallest angle; and the “middle” length side is across from the “middle” sized angle.

More Examples Based on the side lengths given, list the angles in order from least to greatest. #3 C 8 cm 6 cm B A 10 cm Smallest angle is . The “middle” angle is . The largest angle is .

#4 Based on the given angle measures, list the sides in order from shortest to greatest. P The shortest side is . The “middle” side is . The longest side is . 40˚ 110˚ 30˚ R Q

Remember Exterior Angles of Triangles? What are exterior angles? remote interior angles exterior angle

Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

Complete the Lesson Check exercises 1-5 on page 328.

Your Assignment… Page 328 (6-32 evens, 33-39 all)

Exit Pass Name the shortest side in the figure.