Algebal review 5 pdf

Pythagorean triples are important because they help you identify right triangles and identify the lengths of

the sides of right triangles.

Example

What is the measure of ∠a in the triangle below?

Because this triangle shows a Pythagorean triple (3:4:5), you know it is a right triangle. Therefore, ∠a must

measure 90°.

Example

A right triangle has a leg of 8 and a hypotenuse of 10. What is the length of the other leg?

Because this triangle is a right triangle, you know its measurements obey the Pythagorean theorem. You could

plug 8 and 10 into the formula and solve for the missing leg, but you don’t have to. The triangle shows two parts

of a Pythagorean triple (?:8:10), so you know that the missing leg must complete the triple. Therefore, the sec￾ond leg has a length of 6.

It is useful to memorize a few of the smallest Pythagorean triples:

3:4:5 32 + 42 = 52

6:8:10 62 + 82 = 102

5:12:13 52 + 122 = 132

7:24:25 72 + 242 = 252

8:15:17 82 + 152 = 172

8 10

?

3 5

a

4

–GEOMETRY REVIEW–

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