Section 5-5: Inequities in Triangles March 8, 2012

Warm-up 1: Review (10 mins) p. 263, #1-8 Plus:  Draw a Perpendicular Bisector, Angle Bisector, Altitude, and Median in these triangles:  Complete the chart (handout), without looking at your chart.

Warm-up 1: Review

Quiz: 20 minutes Warm-Up 2: Begin when you finish the Quiz: Practice 5-4: p. 60, #1-5, 11-17

Warm-up 2

Questions on Homework?

Section 5-5: Inequities in Triangles  Objectives: Today you will learn to use inequalities involving angles and sides of triangles.

Section 5-5: Comparison Property If a = b + c and c > 0, then a > b

Section 5-5: Corollary Corollary to the Triangle Exterior Angle Theorem (p. 274): The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

Section 5-5: Corollary Example 1:  What is m ∠ 1?  Is m ∠ 1 > m ∠ A?  Is m ∠ 1 > m ∠ B?

Section 5-5: Theorem 5-10 Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

Section 5-5: Theorem 5-10 Example 2: List the angles from smallest to largest

Section 5-5: Theorem 5-11 Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the largest angle.

Section 5-5: Theorem 5-11 Example 3: List the sides from longest to smallest

Section 5-5: Theorem 5-11 Indirect Proof of Theorem 5-11 (p. 275)  Given: m ∠ A > m ∠ B  Prove: BC > AC  Step 1: Assume BC ≤ AC  Step 2: If BC ≤ AC, then m ∠ A m ∠ B is Given, so this is a contraction.  Step 3: The assumption BC ≤ AC must be false, so BC > AC must be true.

Section 5-5: Investigation 1 1.Draw a triangle on a separate piece of paper and label the points. 2.Measure each side and write it down. 3.Add the measurements of each pair of sides (3 pairs). 4.Compare the sum of each pair to the third side. 5.What do you notice?

Section 5-5: Investigation 2 Find the following lengths: AB BC CA Find the following sums: AB + BC AB + CA BC + CA Compare to third side

Section 5-5: Theorem 5-12 Theorem 5-12: Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Section 5-5: Theorem 5-12 Example 4: Can a triangle have sides with the following lengths?  a) 3 ft, 7 ft., 8 ft.  b) 3 cm, 6cm, 10cm  c) 2m, 7m, 9m  d) 4 yd, 6 yd, 9 yd

Section 5-5: Theorem 5-12 Example 5: If a triangle has lengths 8m and 10m, what is the possible range of lengths for the third side (x)?

Section 5-5: Theorem 5-12 Example 6: If a triangle has lengths 3cm and 12cm, what is the possible range of lengths for the third side?

Wrap-up  Today you learned to use inequalities involving angles and sides of triangles.  Tomorrow we’ll review for the test on Monday. Bring your questions!  Homework pp , #4-27, 32, 34-37