Bellwork 1) AG = 18 cm. What is AD? 2) Solve for x.

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Presentation transcript:

Bellwork 1) AG = 18 cm. What is AD? 2) Solve for x.

5-5 Inequalities in Triangles Rigor - Apply inequality theorems to triangles Relevance – Positioning and design

Ordering sides and angles Theorem – If 2 sides of a triangle are not congruent, then the larger angle is opposite the longer side and vice versa. EX 1: Order the sides from shortest to longest

Examples 2 and 3: 2) Order the angles from largest to smallest.

Honors: Workbook Examples Turn to workbook page 215 - 216 and complete examples 1 & 2.

Can any 3 lengths make a triangle? Let’s explore! Break into groups of 4 Find 3 color combinations that WILL connect to make a triangle. Record the colors used. Find 3 color combinations that will NOT connect to make a triangle. Record the colors used. Make a conjecture to the rule that must apply for 3 lengths to form the sides of a triangle.

Triangle Inequality Theorem – the sum of the lengths of 2 sides of a triangle is greater than the length of the 3rd side. Small + medium > large EX 4: Can the 3 lengths form a triangle? A) 3ft, 7ft, 12ft B) 5in, 4in, 3in C) 1m, 3m, 2m

Finding the Range of Possible Side Lengths of a Triangle EX 5: A triangle has side lengths of 9 in and 6 in. What is the range of possible lengths for the third side? 2 options: the third side either is or is not the longest side. Difference < x < Sum 9-6 < x < 9 + 6

EX 7: What is the range of possible lengths for the third side of the triangle? C) 13, 13, ?

5-5 Classwork Textbook pg 348 – 349 #18 – 21, 26, 28, 33 - 35