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____ ___ ___ ____ ___ Applications: Pythagorean Theorem Notes Key Concept: Identifying Parts of Triangle: • Legs: 2 sides forming right angle (a, b) • Hypotenuse: side opposite the right angle; longest side of triangle (c) Leg (a) {N hypotenuse (c) f l eg (b) Example: Identifying Parts of Triangle identify the legs and hypotenuse of the foiiowing right triangles: 17 Legs: 8, 15 (make up right L) 8 Hypotenuse: 17 (largest # & opposite right L) Provided below are lengths of a right triangle. Identify the legs and hypotenuse. • 6,10, 8 Hypotenuse: 10 (largest), Legs: 6 and 8 • 9, 12, 15 Hypotenuse: 15 (largest), Legs: 9 and 12 Practice: Identifying Parts of Triangle Identify the legs and hypotenuse of the following right triangles: 5 3 30 Provided below are lengths of a right triangle. Identify the legs and hypotenuse. a. 12,13, 5 Hypotenuse:____ Legs: and b. 9, 12, 15 Hypotenuse:____ Legs: and c. 25, 7, 24 Hypotenuse:___ Legs: and App: Pythagorean Theorem I Applications: Pythagorean Theorem Notes Key Concept: Pythagorean Theorem 2 (for right angles) 2 =c 2+b o Pythagorean theorem: a • Pythagorean Theorem is used to find the length of a side of a right triangle when the lengths of the other 2 sides are known. -‘-C=3 D=41 2 2 2 e then 2 2 iTa-s-D=c iT3+4-= D then f=\/52=5 2 \/U+h_C_C a=3 or or if 32 = then 3 if a 2 5242 = then a = - = 2 a 2 b = Examples: Solve for Missing Side Using the Pythagorean Theorem, solve for the missing side: x 6 Step 1: Identify legs & hypotenuse Hypotenuse: c = x, Legs: a=6, b=8 8 Step 2: Pluq in values 62 + 8= x 2 in a 2 + 2 b = 2 and solve c 64=x 2 36+ 100=x 2 10 =x Step 1: identify legs & hypotenuse Hypotenuse: c = 17, Legs: ax, b15 x h 15 Step 2: Plug in values = 172 52 289 -225 =64 2 x x=8 = App: Pythagorean Theorem in a 2 = - 2 and solve b Applications: Pythagorean Theorem Notes Practice: Solve for Missing Side Using the Fythagorean Theorem, solve for the missing side: 1. Solve for a 2. Solve for c 10 3. Solve for b 24 2 C b 4. Solve for a 10 a 5. Solve for c 5 6. Solve for b 4 b Key Concept: Determining if lengths are sides of right triangle . When given 3 sides, identify your hypotenuse and legs with the . . hypotenuse being the largest number, Plug in values into the Pythagorean Theorem: a 2+b 2 If the equation is true, then you have a right triangle = Examples: Determining if lengths are sides of right triangle Determine whether the given lengths are sides of a right triangle. a.3,9,6 b.6,1O,8 h’potenuse: 9; legs: 3, 6 hypotenuse: 10; legs 6, 8 3+62=92 64÷82=102 9+36=81 45 81 No 36+64=100 100 =100 Yes App: Pythagorean Theorem 3 Applications: Pythagorean Theorem Notes Practice: Determining if lengths are sides of right triangle Determine whether the given lengths are sides of a right triangle. c.7,24,25 b16,30,34 a20,21,29 d. 24, 60, 66 e. 23,18,14 f. 9, 12, 15 Key Concept: Pythagorean Triples There are many common sets of 3 whole numbers that satisfy the Pythagorean Theorem. Memorize the following Pythagorean Triples. They corn•e in handy and help save you time. • 3,4,5 .5,12,13 • 7,24,25 • 8,15,17 NOTE: The largest number must be the hypotenuse in order for these to work. Key Concept: Special Right Triangles //4\ I App: Pythagorean Theorem 4