Triangle abc a²a² b²b² c²c² Blue* Green Orange* Pink Purple* White* Yellow*

Pythagoras and his Theorem Right Triangle: a triangle with exactly one right angle. Legs: the sides of a triangle that form the right angle. Hypotenuse: the longest side, its located across from the right angle.

c a b The legs are labeled a & b and the hypotenuse is ALWAYS labeled c.

Pythagoras discovered that the sum of the squares of the two legs in a right triangle is equal to the square of the hypotenuse. That means, in any right triangle, a² + b² = c² leg² + leg² = hypotenuse²

The term “squared” comes from the area of a square. EX: 3 “squared” means 3x3 or 9. The area of a 3x3 square is 9

Could a right triangle have sides that measure 3 cm, 4 cm, and 5 cm? a² + b² = c² 3² + 4² ? 5² ? = 25 Yes, this is a right triangle because the Pythagorean Theorem works!

How about sides of 5, 6, and 7? a² + b² = c² 5² + 6² ? 7² ? ≠ 49 NO, this is a NOT right triangle because the Pythagorean Theorem doesn’t work!

Is 15, 17, 8 a right triangle? Why or why not? Show Work! a² + b² = c² 8² + 15² ? 17² ? = 289 Yes, this is a right triangle because the Pythagorean Theorem works!

Using the Pythagorean Theorem to Find a Missing Side Note: the missing side is the hypotenuse a² + b² = c² 5² + 12² = c² = c² 169 = c² √169 = √c² 13 = c

What if you know the hypotenuse? You can use the theorem to find one of the legs. a² + b² = c² 9² + b² = 15² 81 + b² = b² = 144 √b² = √144 b = 12

TENTH When your answers don’t work out evenly, round to the nearest TENTH. a² + b² = c² a² + 4² = 11² a² + 16 = b² = 105 √b² = √105 b = m

Finally, we can use the Pythagorean Theorem to solve real life word problems. Jen hiked 8 miles east, then turned and hiked 6 miles south. How far was she from her starting point? DRAW A PICTURE!

Jen hiked 8 miles east, then turned and hiked 6 miles south. How far was she from her starting point? 8 miles east 6 miles south ? a² + b² = c² 8² + 6² = c² = c² 100 = c² √100 = √c² 10 = c Jen was 10 miles from where she started.

Polygons Polygon: a closed figure formed by 3 or more line segments that intersect only at their verticies. Polygons are classified by the number of sides and angles they have

Polygons 3 sides: triangle 4 sides: quadrilateral 6 sides: hexagon 5 sides: pentagon 7 sides: heptagon 10 sides: decagon 9 sides: nonagon 8 sides: 8 sides:octagon

Regular Polygons Regular Polygon: a polygon in which all the sides are the same length and all the angles are the same measure. Example:

Interior Angles Sum of Interior Angle Formula: (n – 2) * 180 What if we wanted to know the measure of EACH interior angle of a regular pentagon? How would we go about doing this? Discuss with your partner.

Find the measure of each interior angle of a pentagon. 108º

Find the measure of each interior angle of a hexagon. 120º

How many sides does a polygon have if the sum of its interior angles is 1440º. 10 sides

Find the measure of the missing angle in the figure below. 93º