Pythagorean Theorem Triangles: 3 sides, 3 angles sum of angles = 180

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Presentation transcript:

Pythagorean Theorem Triangles: 3 sides, 3 angles sum of angles = 180 Acute, Obtuse, or Right Scalene, Isosceles, or Equilateral

Classifying triangles by sides: Equilateral Triangle: all sides equal length 3 in 3 in 3 in Isosceles Triangle : two sides equal in length Scalene Triangle: no sides equal 22 cm 8 cm 16 cm

Classifying Triangles by Angles: Acute Triangles: all three angles are acute (less than 90°) 35° 80° 65° Obtuse Triangle: ONE obtuse angle (greater than 90°) 18° 135° 27° Right Triangle: one right angle = 90° Equiangular: All angles equal, which means all angles are . . .

Right Triangles: 2 legs ( two sides that make right angle) 1 Hypotenuse (side across from right angle – always the longest of the three sides) Ex. a c b Legs are sides a and b Hypotenuse is side c

Pythagorean Theorem: In all right triangles a2 +b2 = c2 Where a and b are the legs and c is the hypotenuse. a c b Can ONLY be a right Triangle if Pythagorean Theorem holds TRUE.

Ex. Can the following measurements represent the sides of a right triangle? 2 ft., 5ft, 7 ft. a = 2 , b = 5 , c = 7 (c is always longest side) a2 +b2 = c2 22 + 52 = 72 4 + 25 = 49 29 = 49 FALSE – So, 2ft, 5 ft, and 7ft, cannot create three sides that form a right triangle. (can form a triangle, just not a RIGHT triangle)

2) Find the missing side of the triangle. 6in x 8 in a2 +b2 = c2 62 + 82 = x2 36 + 64 = x2 100 = x2   10 in = x

Find the missing side. 3)18ft x 30 ft a2 +b2 = c2 182 + b2 = 302 324 + b2 = 900 324 + b2 – 324 = 900-324 b2 = 576   b = 24 ft

4) p.467, #6 a2 +b2 = c2 52 + b2 = 152 25 + b2 = 225 25 + b2 – 25 = 225 - 25 b2 = 200 15 ft 5 ft   15 ft b = 14.14 b = 14 ft rounded to nearest foot 5 ft

The distance between Mr. Stoner and Mr. Foltz houses is 36.4 miles. Mr. Stoner helped Mr. Foltz build his tree stand on Saturday. Mr. Stoner drove 10 miles north and 35 miles west to travel from his house to Mr. Foltz’s. What is the distance between their houses? Mr. Foltz’s House a2 + b2 =c2 102 + 352 = c2 100 + 1225 = c2 1325 = c2 35 miles west 10 miles north Dist. Between houses 36.4 = c Mr. Stoner’s House The distance between Mr. Stoner and Mr. Foltz houses is 36.4 miles.

Mall Walmart a2 + b2 = c2 102 + 92 = x 2 100 + 81 = x2 181 = x2 What is the distance between Walmart and the mall? What direction do you travel to go from the Mall to Walmart? Mall Walmart a2 + b2 = c2 102 + 92 = x 2 100 + 81 = x2 181 = x2 13.5 = x

Homework : worksheet