4.4 Pythagorean Triples & Fraction Review

A Pythagorean Triple consists of three positive integers a, b, and c, such that $$a^2 + b^2 = c^2$$ . For example, (3, 4, 5) is a Pythagorean Triple.

To divide fractions, multiply the first fraction by the reciprocal of the second. For example, $$\frac{1}{3} \div \frac{5}{7} = \frac{1}{3} \times \frac{7}{5} = \frac{7}{15}$$ .

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): $$a^2 + b^2 = c^2$$ .

Yes, because $$9^2 + 12^2 = 15^2$$ (81 + 144 = 225).

To multiply fractions, multiply the numerators together and the denominators together. For example, $$\frac{2}{5} \cdot \frac{1}{6} = \frac{2 \cdot 1}{5 \cdot 6} = \frac{2}{30}$$ .

Use the Pythagorean Theorem: $$c = \sqrt{a^2 + b^2}$$ , where c is the hypotenuse and a and b are the other two sides.

a = 12, because $$12^2 + 35^2 = 37^2$$ (144 + 1225 = 1369).

A fraction represents a part of a whole and is expressed as $$\frac{a}{b}$$ , where a is the numerator and b is the denominator.

A right triangle has one angle that measures 90 degrees.

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ .