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RIGHT TRIANGLES

Right triangles are triangles in which one of the interior angles is 90o. A 90o angle is called a right angle. Right triangles are sometimes called right-angled triangles. The other two interior angles are complementary, i.e. their sum equals 90o. Right triangles have special properties which make it easier to conceptualize and calculate their parameters in many cases.

The side opposite of the right angle is called the hypotenuse. The sides adjacent to the right angle are the legs. When using the Pythagorean Theorem, the hypotenuse or its length is often labelled with a lower case c. The legs (or their lengths) are often labelled a or b.

Either of the legs can be considered a base and the other leg would be considered the height (or altitude), because the right angle automatically makes them perpendicular. If the lengths of both the legs are known, then by setting one of these sides as the base ( b ) and the other as the height ( h ), the area of the right triangle is very easy to calculate using this formula:

(1/2)

THEOREMS

The converse of the 30-60-90 Triangle Theorem

If in a right triangle, one leg is half as long as the hypotenuse, then the opposite angle has a measure of 30

The converse of the 30-60-90 Triangle Theorem

If in a right triangle, one leg is half as long as the hypotenuse, then the opposite angle has a measure of 30

The converse of the Pythagorean theorem

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides , then the triangle is a right triangle and the right angle is opposite the longest side.

The converse of the Pythagorean theorem

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides , then the triangle is a right triangle and the right angle is opposite the longest side.

The median theorem

The median to the hypotenuse of a right triangle is one-half as long as...

Right triangles are triangles in which one of the interior angles is 90o. A 90o angle is called a right angle. Right triangles are sometimes called right-angled triangles. The other two interior angles are complementary, i.e. their sum equals 90o. Right triangles have special properties which make it easier to conceptualize and calculate their parameters in many cases.

The side opposite of the right angle is called the hypotenuse. The sides adjacent to the right angle are the legs. When using the Pythagorean Theorem, the hypotenuse or its length is often labelled with a lower case c. The legs (or their lengths) are often labelled a or b.

Either of the legs can be considered a base and the other leg would be considered the height (or altitude), because the right angle automatically makes them perpendicular. If the lengths of both the legs are known, then by setting one of these sides as the base ( b ) and the other as the height ( h ), the area of the right triangle is very easy to calculate using this formula:

(1/2)

THEOREMS

The converse of the 30-60-90 Triangle Theorem

If in a right triangle, one leg is half as long as the hypotenuse, then the opposite angle has a measure of 30

The converse of the 30-60-90 Triangle Theorem

If in a right triangle, one leg is half as long as the hypotenuse, then the opposite angle has a measure of 30

The converse of the Pythagorean theorem

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides , then the triangle is a right triangle and the right angle is opposite the longest side.

The converse of the Pythagorean theorem

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides , then the triangle is a right triangle and the right angle is opposite the longest side.

The median theorem

The median to the hypotenuse of a right triangle is one-half as long as...

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