Geometry Ch 8 - Right Triangles & Trigonometry

Question 1

Pythagorean Theorem

Answer 1

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.

a² + b² = c²

Question 2

Pythagorean Triple

Answer 2

A set of nonzero, whole numbers a, b, c that satisfy the equation a² + b² = c². If you multiple the three numbers in a Pythagorean triple by the same whole number, the the three numbers that result will also form a Pythagorean triple.

Common examples:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

Question 3

Converse of the Pythagorean Theorem

Answer 3

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.

Question 4

If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides…

Answer 4

… the triangle is obtuse.

i.e. If c² > a² + b², then the triangle is obtuse.

Question 5

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides…

Answer 5

… the triangle is acute.

i.e. If c² < a² + b², then the triangle is acute.

Question 6

45º-45º-90º Triangle Theorem

Answer 6

In a 45º-45º-90º triangle, both legs are congruent and the length of the hypotenuse is √2 times the length of a leg.

Question 7

30º-60º-90º Triangle Theorem

Answer 7

In a 30º-60º-90º triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.

Question 8

tan A (pronounced “tangent of A”)

Answer 8

tan A = opposite / adjacent