Cathetus . It comes from the Greek Kathetos, which means “that falls perpendicular. In plane geometry , it is either side of a right triangle that make up the right angle , that is, 90 degrees.
Summary
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- 1 Cathetus Theorem
- 2 Pythagorean Theorem
- 1 Comparisons
- 2 Orthocenter
- 3 Source
Cathetus theorem
In a right triangle a leg is a proportional mean between the hypotenuse and its projection on it.
- a is the hypotenuse
- b and c are the legs
- m is the projection of leg b on the hypotenuse
- n is the projection of leg c on the hypotenuse
Pythagoras theorem
The square of the length of the hypotenuse is equal to the sum of the square of the lengths of the legs.
a² = c² + b²
Comparisons
From a² = c² + b², it follows that a²> c² and a²> b² (the sum is greater than any sum in positives) and in turn a> c and> b (the square root preserves the order). In both possibilities, the hypotenuse is greater than any of the legs.
Since the angles opposite the legs add up to 90º, any of the acute angles measures less than 90º. The greater the angle, the greater the opposite side, then the hypotenuse that opposes the right angle is greater than either of the two legs.
Orthocenter
One leg is perpendicular to the other leg and this one to the first. Then a leg, when joining a vertex with the opposite side and being perpendicular to the other, is also height. Furthermore, it can be shown that the other leg is height. The height corresponding to the hypotenuse starts from the vertex of the right angle, so that the three heights of the right triangle meet at the vertex of the right angle and this vertex becomes the orthocenter of a right triangle.
Area
- The area of a right triangle can be expressed as the semi-finished product of the legs, considering one of them as the base and the other as height. A = 0.5bc.
- The previous area can also be deduced from A = 0.5 bcsen A. where A = 90º, and its sine = 1.
