* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 5.5 Inequalities in one triangle
Survey
Document related concepts
Technical drawing wikipedia , lookup
Penrose tiling wikipedia , lookup
Multilateration wikipedia , lookup
History of geometry wikipedia , lookup
Golden ratio wikipedia , lookup
Apollonian network wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euclidean geometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
Transcript
Notes 5-5: Inequalities in One Triangle Objectives: Geometry - Ch. 5: Properties and Attributes of Triangles Apply inequalities in one triangle. Angle & Side Relationships in Triangles: in a triangle, the largest side is opposite the ____________________ angle. Similarly, the smallest side is opposite the ____________________ angle. The ____________________ of each of these is also true. EX 1: Write the angles in order from smallest to largest. a) ______ < ______ < ______ (a) (b) (a) (b) b) ______ < ______ < ______ EX 2: Write the sides in order from smallest to largest. a) ______ < ______ < ______ b) ______ < ______ < ______ Investigate: Will the following lengths create a triangle? 3 7 4 4 4 7 7 Triangle Inequality Theorem: in a triangle, the sum of any two sides is ____________________ than the third. ______ + ______ > ______ ______ + ______ > ______ ______ + ______ > ______ Trick: if 3 lengths can create a triangle, the __________ of the 2 smaller sides should be ________ than the 3rd. EX 3: Can the following set of side lengths create a triangle? a) 7, 10, 19 b) 2.3, 3.1, 4.6 ________ ________ EX 4: The lengths of two sides of a triangle are 17 & 22 inches. Find the range of possible lengths for the third side. _____ < x < _____ c) t - 2 , 4t , t2 + 1 when t =4 ________ EX 5: Find the possible range of distances between San Francisco and Oakland. _____ < x < ____