5. 6 Inequalities in One Triangle.notebook
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5. 6 Inequalities in One Triangle.notebook 1 October 27, 2017 Warm Up Classify the triangles with side lengths: a. 4, 10, 13 b. 5, 12, 13 c. 6, 11, 12
Transcript of 5. 6 Inequalities in One Triangle.notebook
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Warm UpClassify the triangles with side lengths:
a. 4, 10, 13 b. 5, 12, 13 c. 6, 11, 12
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Learning Goal: Today I will learn how sides and angles are related.
Success Criteria: I am able to find the largest/smallest side or angle of a triangle.
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5.6 Inequalities in One Triangle
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*Theorems 510 and 511Theorem If Then
Two sides of a triangle that are not congruent, the larger angle lies opposite the longer side
Two angles of a triangle are not
congruent, the longer side is opposite the
larger angle
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Using the Theorems
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Using the Theorems
List the sides from shortest to longest
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*Triangle Inequality Theorem
Theorem
The sum of the lengths of any 2 sides of a
triangle are greater than the length of the
remaining (third) side.
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One piece of spaghetti, rulerNeed:
Break off 4cm, 5 cm and 10 cm
Move the pieces around until you form a triangle.
What do you notice? Why?
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For three segments to form a triangle, their lengths must be related in a certain way. Notice that only one of the sets of segments below can form a triangle.
The sum of the smallest two lengths must be greater than the greatest length.
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To find what the possible sides could be, you write each one as an inequality. Use
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Using the Triangle Inequality Theorem
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To find what the possible sides could be, you write each one as an inequality. Use the property that will allow you to get each of these.
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Using the Triangle Inequality Theorem
A triangle has side lengths of 5ft and 8ft. What is the range of possible side lengths?Let x represent the length of the third side.
So x must be greater than 3 and less than 13
3 < x < 13
5 + x > 8 8 + x > 5 5 + 8 > x
Use your sides given and put each of them in an inequality.a + x > b b + x > a a + b > x This will give us one that does not work and two that work. To create our high and low for the inequality.
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Now find the range that you can make for the 4 cm and 5 cm.
Pick a number in that range and test to see if you get a triangle.
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Closure: Today I learned how to order side lengths and angles.
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