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1/17/2017 65 Upcoming Dates • 1/16 (Mon) • 1/18 (Wed) Unit 7 SCHOOL HOLIDAY Major Quiz on Triangles 66 67 Angles in Triangles Pythagorean Theorem (Angles & Pythagorean Theorem) 65 Unit 7: Words To Know • Right triangle – triangle with 1 right angle and 2 acute angles • Legs of a right triangle – 2 shortest sides of a right triangle; sides that form the right angle • Hypotenuse – longest side of right triangle; side opposite the right angle On your graph paper: • Draw a right triangle in the center with legs of 3 units and 4 units. • Draw a square that has a side length of 3 units in the lower left corner. Write its area inside. • Draw a square that has a side length of 4 units in the lower right corner. Write its area inside. • Add the 2 areas together, and draw a square with that area in the top right corner. Pythagoras • Born in Greece in 569 B.C. • Is known as the Father of Numbers. • Traveled extensively in Egypt, learning math, astronomy, and music. • Urged citizens of Croton to follow his religious, political, and philosophical goals. • His followers were known as Pythagoreans. They had to observe a rule of silence for five years before they could contribute to the group. Breaking this silence was punishable by death! The sum of the squares of the shortest sides is equal to the square of the longest side. 1 1/17/2017 Pythagorean Theorem Is it a right triangle? • Used to find a missing side length of a RIGHT triangle. 𝑎 = 5, 𝑏 = 12, 𝑐 = 13 Hypotenuse 𝑎 = 7, 𝑏 = 8, 𝑐 = 12 Legs 𝑎2 + 𝑏2 = 𝑐 2, where 𝑎 and 𝑏 are legs, and 𝑐 is the hypotenuse Reminder: The inverse operation of a square (𝑥 2 ) is a square root ( 𝑥). Is it a right triangle? 𝑎 = 6, 𝑏 = 8, 𝑐 = 10 12 cm 𝑥 35 cm 𝑎 = 4, 𝑏 = 8, 𝑐 = 9 28 m 35 m 𝑥 24 in 25 in 𝑥 12 in 𝑥 16 in 2