Instructional Unit for Geometry


By Brook Buckelew and Nikki Masson


Right Triangles and Trigonometry

Lesson 3/ Day 3

The Converse of the Pythagorean Theorem



Theorem:(Converse of the Pythagorean Theorem) - If a triangle has sides of lengths a, b and c where c is the longest length and c^2 = a^2 + b^2, then the triangle is a right triangle with c its hypotenuse.


Variations of the Converse of the Pythagorean Theorem can be used to classify a triangle as right, obtuse, or acute.


Theorem: If a, b, and c represent the lengths of the sides of a triangle, and c is the longest length, then the triangle is obtuse if c^2 > a^2 + b^2, and the triangle is acute if c^2 < a^2 + b^2.



Sample Problems:

Example 1:

Proof: Prove that a, b, and c are a Pythagorean triple, then ka, kb, and kc (where k > 0) represent the side lengths of a right triangle.




Example 2:

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