Chapter 10 Pythagorean Theorem. hypotenuse Leg C – 88 In a right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse,

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Presentation transcript:

Chapter 10 Pythagorean Theorem

hypotenuse Leg

C – 88 In a right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse, then a 2 + b 2 = c 2 (Pythagorean Theorem)

Lesson 10.2 C – 89 If the lengths of the three sides of a triangle work in the Pythagorean formula then the triangle is a right triangle. (Converse of the Pythagorean Theorem)

Lesson 10.4 C – 90 In an isosceles right triangle, if the legs have length x, then the hypotenuse has length x x

C – 91 In a right triangle, if the side opposite the 30º angle has length x, then the hypotenuse has length 2x. C – 92 In a right triangle, if the shorter leg has length x, then the longer leg has length and the hypotenuse has length 2x. (30-60 right triangle conjecture)

60 30 x 2x

Lesson 10.5 C – 93 If you multiply the lengths of all three sides of any right triangle by the same number, the resulting triangle will be a right triangle. (Pythagorean Multiples conjecture) C – 94 If the lengths of two sides of a right triangle have a common factor, then the third side also has that factor.

Right triangles

Lesson 10.7 C – 95 If the coordinates of points A and B are (x 1,y 1 ) and (x 2,y 2 ), respectively, then AB 2 = (x 1 – x 2 ) 2 + (y 1 – y 2 ) 2 and (Distance Formula)

C – 96 The equation for a circle with radius r and center (h, k) is (x – h) 2 +(y – k) 2 = r 2 (Equation of a circle)

Lesson 10.8 A tangent to a circle is perpendicular to the radius drawn to the point of tangency. (Tangent Conjecture) Angles inscribed in a semicircle are right angles. (C-70)