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Chapter 7 - Geo.

Chapter 7 Theorems/Collaries/Postulates

QuestionAnswer
Pythagorean Theorem in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
Converse of Pythagorean Theorem if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle
Geometric Mean (Altitude) Theorem If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle
45-45-90 Triangle Theorem In a 45-45-90 triangle, the hypotenuse is the square root of 2 times as long as each leg
30-60-90 Triangle Theorem in a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other
Geometric Mean (Leg) Theorem in a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments; the length of each leg of the right triangle is the geometric mean of the lengths of hypotenuse and the segment of the hypotenuse that is
adjacent to the leg
Created by: kgatling