7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE

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Presentation transcript:

7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE GEOMETRY

Pythagorean Theorem (Thm Pythagorean Theorem (Thm. 7-4): In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. 𝑎 2 + 𝑏 2 = 𝑐 2

Pythagorean Triple: set of nonzero whole numbers, a, b, and c that satisfy the Pythagorean Theorem Common Triples: 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17 12, 25, 37 20, 21, 29

Ex. 1) Are 6, 8, and 15 a Pythagorean Triple?

Ex. 2) Find the variable.

Ex. 3) Find the variable.

Ex. 4) Find the variable.

Ex. 5) Finding the Area using the Pythagorean Thm.

𝑎 2 + 𝑏 2 = 𝑐 2 𝑎 2 + 𝑏 2 > 𝑐 2 𝑎 2 + 𝑏 2 < 𝑐 2 Converse of the Pythagorean Theorem (Thm. 7-5): If the square of the length of one 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. 𝑎 2 + 𝑏 2 = 𝑐 2 𝑎 2 + 𝑏 2 > 𝑐 2 𝑎 2 + 𝑏 2 < 𝑐 2 Right Triangle Acute Triangle Obtuse Triangle

Ex. 6) Classify the triangle.

Ex. 7)