Presentation on theme: "What is the Triangle Inequality Theorem?"— Presentation transcript:
1What is the Triangle Inequality Theorem? The Triangle Inequality Theorem states thatthe sum ofANY 2 SIDESof a triangle must beGREATER thanthe measure of the 3rd side.
2Can multiple triangles have the same angle measures? YES! Similar triangles are triangles whose sides are proportionate and the angles are CONGRUENT!
3Test 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 cm3 + 4 = 7 greater than 64 + 6 = 10 greater than 33 + 6 = 9 greater than 4So…Since each two sums are greater than the third,it can be a triangle.
4Do you really have to test all 3 sides? No.Just add the two shortest sides.They must be greater than the longest side.
5Summarize 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.
6What is the formula for finding area of a triangle?
8Solve for missing angle measure. Write an equation to solve for the missing angle measure.
9Solve for the missing angle measure. Write an equation to solve for x first.Then you can find the missing angle measure.
10What do you need to know about geometry? G2 – Draw (freehand & w/ tech) geometric shapesG2 - sum of all the angles in a triangleG2 - 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 anglesG6 – Solve real-world prob with area, volume, surface area of 2D & 3D objects including triangles, quadrilaterals, polygons, cubes, and right prisms.
11Determine all the unknown measures in the figure. Handouts included. m < Mm < xm < y
12Triangle Inequality Theorem Could these be the lengths of a triangle?4, 8, 25, 6, 76, 8, 157, 9, 15