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What is the Triangle Inequality Theorem?

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Presentation on theme: "What is the Triangle Inequality Theorem?"— Presentation transcript:

1 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.

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

3 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.

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

5 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.

6 What is the formula for finding
area of a triangle?

7 What is the sum of all angles in any triangle?

8 Solve for missing angle measure.
Write an equation to solve for the missing angle measure.

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

10 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.

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

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










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