Objective: (same as Day 7)

GA QCC: #24

Lesson: Pythagorean Converse

Name: ___________________________

1. Form the previous lesson (Day 7), we learned the Pythagorean Theorem. As a result of working with the theorem, there are sets of positive numbers which satisfy the theorem. Those sets of numbers are called Pythagorean triples. Common triples are

3, 4, and 5

5, 12, and 13

7, 24, and 25 and

the multiples of those sets (for example, 6, 8, 10 and 10, 24, 26).

2. The converse of the theorem can be stated as follows:

If the square of the longest side of a triangle is equal to the sum of squares of the 2 shorter sides, then the triangle is a right triangle.

3. CLICK HERE for experimentation. Notice that if you change the right angle (angle A), then the sums of the squares of the the 2 shorter sides do not add up to the square of the longest side.

4. Problems: Decide if the numbers are a Pythagorean triple:

4a. 9, 40, and 41. Answer: _______________

4b. 10, 49, and 50. Answer: __________________

4c. 15, 36, and 39. Answer: __________________

5. Are the following triangle lengths the measurements of a right triangle?

5a. 4, , and 9. Answer: _______________

5b. , 6, and 7. Answer: ________________

5c. 2, 3, and . Answer: _________________

6. You are making the forms for a concrete pad to hold a piece of equipment. As a matter of pride, you want to make sure that at least 2 adjacent angles are exactly right angles. If the 2 adjacent sides are 9 feet and 12 feet, and you only have your Home Depot (or was it Lowes?) retractable, metal tape measure, how can you ensure that the angles are exactly 90 degrees?

Answer: __________________________________________________

_________________________________________________________

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