Hachie Chapter 8

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.

Question 2

Converse of the Pythagorean Theorem

Answer 2

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 3

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 3

then the triangle is obtuse

Question 4

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 4

then the triangle is acute

Question 5

In a 45-45-90 triangle

Answer 5

both legs are congruent and the length of the hypotenuse is the square root of 2 times the length of a leg.

Question 6

In a 30-60-90 triangle

Answer 6

the length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is the square root of 3 times the length of the shorter leg.