Similar Right triangles

Theorem 7.5

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to eachother

Theorem 7.3

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 2 sides, then it's an acute triangle

Theorem 7.4

If the square of the length of the longest side of a triangle is more than the sum of the squares of the lengths of the other 2 sides, then it's an obtuse triangle

Theorem 7.9/ 30-60-90

In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, the longer leg is 3 rooted times as long as the shorter leg

Theorem 7.8/45-45-90

In a 45-45-90 triangle, the hypotenuse is 2 rooted times as long as each leg

Theorem 7.1 Pythagorean theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the legs

Pythagorean Triple

A set of three positive integers a, b, c that satisfy the theorem

Practice

To identify similar triangles: 1) Break apart the triangles 2) Set up ratios and solve

Theorem 7.2

Converse pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other 2 sides, then it's a right triangle

Isosceles triangles

To find the area of an Isosceles triangle 1) Use Pythag. Theorem to find the height 2) Find the area