Geometry Chapter 8

Front 1

If a, b, and x are positive numbers and a/x=x/b then x is called the

Back 1

geometric mean between a and b.

Front 2

Theorem 8-1

Back 2

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

Front 3

Corollary 8-1

Back 3

When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.

Front 4

Corollary 8-2

Back 4

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

Front 5

Theorem 8-2/Pythagorean Theorem

Back 5

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

Front 6

Theorem 8-3

Back 6

If the square of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle

Front 7

Theorem 8-4

Back 7

If c^2<a^2+b^2 then m<c is less than 90 and the triangle is acute

Front 8

Theorem 8-5

Back 8

If c^2>a^2+b^2 then m<c is more than 90 and the triangle is obtuse

Front 9

Theorem 8-6 45-45-90 theorem

Back 9

The legs of a right triangle are equal to each other and the hypotenuse is the leg x root 2

Front 10

Theorem 8-7 30-60-90 theorem

Back 10

The hypotenuse is twice as long as the shortest leg and the bigger leg is equal to the shorter leg x root 3