Presentation on theme: "8.1 Pythagorean Theorem and Its Converse"— Presentation transcript:
1 8.1 Pythagorean Theorem and Its ConverseIf a triangle is a right triangle, then the amount of the squares of the lengths the the legs is same to the square that the size of the hypotenuse. The hypotenuse is always the greatest side of the best triangle. The hypotenuse is always located opposite native the right angle.
2 Finding the length of the HypotenuseWhat is the size of the hypotenuse in Triangle ABC?
3 Simplest Radical type SimplifyTo leveling a number, uncover numbers that enter the larger number that room perfect squares. Example: 4, 9, 16, 25, 36, 49, etc….
4 simplest Radical type Simplify
5 Finding the length of the LegWhat is the value of x? Express your answer in most basic radical form. Remember, the legs have the right to go in for either a or b. The hypotenuse must constantly be letter c.
6 Converse the the Pythagorean TheoremIf the amount of the squares of the lengths of 2 sides that a triangle is equal to the square of the length of the 3rd side, climate the triangle is a right triangle. We usage the converse the the Pythagorean Theorem come PROVE triangle are ideal triangles.
7 Pythagorean Triples A Pythagorean triple is a set of nonzero totality numbers, a, b, and c that constantly satisfy the equation a² + b² = c². Some common Pythagorean Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
8 Classifying ideal Triangles together Obtuse or AcuteTheorem Obtuse – If the square that the size of the longest next of a triangle is better THAN the sum of the squares of the lengths that the other two sides, then the triangle is OBTUSE. Organize Acute – If the square the the length of the longest next of a triangle is less THAN the sum of the squares that the lengths that the various other two sides, then the triangle is ACUTE.
9 Classifying a TriangleA triangle has actually side lengths 6, 11, and 14. Is the acute, obtuse, or right? c² ___ a² + b² 14² ___ 6² + 11² 196 ___ 196 > 157 The triangle is obtuse.
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