What is the Triangle Inequality Theorem?

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Presentation transcript:

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.

Can multiple triangles have the same angle measures? YES! Similar triangles are triangles whose sides are proportionate and the angles are CONGRUENT!

Test the Triangle Inequality Theorem Add each pair of sides to see if it is greater than the third side. Try it with 3 cm, 4 cm, & 6 cm 3 + 4 = 7 greater than 6 4 + 6 = 10 greater than 3 3 + 6 = 9 greater than 4 So…Since each two sums are greater than the third, it can be a triangle.

Do you really have to test all 3 sides? No. Just add the two shortest sides. They must be greater than the longest side.

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.

What is the formula for finding area of a triangle? http://www.mathwarehouse.com/geometry/triangles/interactive-triangle.php

What is the sum of all angles in any triangle?

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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.

Determine all the unknown measures in the figure. Handouts included. m < M m < x m < y

Triangle Inequality Theorem Could these be the lengths of a triangle? 4, 8, 2 5, 6, 7 6, 8, 15 7, 9, 15