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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.

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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!

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**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.

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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.

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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.

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**What is the formula for finding**

area of a triangle?

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

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**Solve for missing angle measure.**

Write an equation to solve for the missing angle 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.

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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.

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

m < M m < x m < y

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**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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Geometry. Triangles Triangle angle sum theorem: the sum of the angles in any triangle is 180° Triangle inequality theorem: the sum of the lengths of any.

Geometry. Triangles Triangle angle sum theorem: the sum of the angles in any triangle is 180° Triangle inequality theorem: the sum of the lengths of any.

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