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What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure of the 3 rd side.

What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 1: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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What is the Triangle Inequality Theorem?

The Triangle Inequality Theorem states that the sum of

ANY 2 SIDES of a triangle must be

GREATER than the measure of the 3rd side.

Page 2: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Can multiple triangles have the same angle measures? YES!

• Similar triangles are triangles whose sides are proportionate and the angles are CONGRUENT!

Page 3: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Test the Triangle Inequality TheoremAdd each pair of sides to see if it is greater than the third side.

Try it with 3 cm, 4 cm, & 6 cm

1. 3 + 4 = 7 greater than 62. 4 + 6 = 10 greater than 33. 3 + 6 = 9 greater than 4

So…Since each two sums are greater than the third,it can be a triangle.

Page 4: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Do you really have to test all 3 sides?

• No.• Just add the two shortest sides.• They must be greater than the longest side.

Page 5: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Summarize our findings on pg. 90 in your book…

• Let’s answer #7 together to summarize the Triangle Inequality Theorem.

• Does 7, 8, and 25 make a triangle?• Is 7+8 > 25?

• Summary statement: To form a triangle, the sum of any two sides must be greater than the 3rd side.

Page 6: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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http://www.mathwarehouse.com/geometry/triangles/interactive-triangle.php

What is the formula for finding area of a triangle?

Page 7: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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What is the sum of all angles in any triangle?

Page 8: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Solve for missing angle measure.

• Write an equation to solve for the missing angle measure.

Page 9: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Solve for the missing angle measure.

• Write an equation to solve for x first. • Then you can find the missing angle measure.

Page 10: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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What do you need to know about geometry?

• G2 – Draw (freehand & w/ tech) geometric shapes• G2 - sum of all the angles in a triangle• G2 - how to test side lengths to see if they form a triangle.• G3 - 2D shapes that result from cross sections of right rectangular

prisms & right rectangular pyramids.• G4 – area & circumference of a circle; know relationship between

Area & Circum.• G5 – Angle pairs - supplementary, complementary, vertical, and

adjacent angles• G6 – Solve real-world prob with area, volume, surface area of 2D

& 3D objects including triangles, quadrilaterals, polygons, cubes, and right prisms.

Page 11: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Determine all the unknown measures in the figure. Handouts included.

1. m 2. m < M3. m < x4. m < y

Page 12: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Triangle Inequality Theorem

Could these be the lengths of a triangle?1. 4, 8, 22. 5, 6, 73. 6, 8, 154. 7, 9, 15

Page 13: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 14: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 15: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 16: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 17: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 18: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 19: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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Page 20: What is the Triangle Inequality Theorem? 1 The Triangle Inequality Theorem states that the sum of ANY 2 SIDES of a triangle must be GREATER than the measure

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