It usually takes a hypotenuse a long time to discover that it is the longest side of a triangle.
He left it to his family as part of his estate, the rest of which consisted of two mules and a hypotenuse of non-arable land.
The main particular applications of the theorem of the square on the hypotenuse (e.
Of propositions attributed to him the most famous is, of course, the theorem that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the sides about the right angle (Eucl.
A, walking from corner to corner, may be said to diangulate the hypotenuse of the meadow.
One week later he decided that he should have cupped his hands and shouted, "You hypotenuse hussy!
Ask me about the square on the hypotenuse of a right-angled triangle.
No, said Lynch, give me the hypotenuse of the Venus of Praxiteles.
You would not write your name in pencil across the hypotenuse of a right-angled triangle.
That triangle contains one of the perpendiculars of three, the base of four, and the hypotenuse of five parts, the square of which is equal to the squares of those sides containing the right angle.
In geometry he is said to have been the first to demonstrate the proposition that the square on the hypotenuse is equal to the sum of the squares upon the other two sides of a right triangle.
Two right triangles are congruent if the hypotenuse and a side of the one are equal respectively to the hypotenuse and a side of the other.
Each of the other sides is the mean proportional between the hypotenuse and the segment of the hypotenuse adjacent to that side.
Two right triangles are congruent if the hypotenuse and an adjacent angle of the one are equal respectively to the hypotenuse and an adjacent angle of the other.
It follows from this corollary, as the pupil has already found, that the mid-point of the hypotenuse of a right triangle is equidistant from the three vertices.
Others have thought that Pythagoras derived his proof from dissecting a square and showing that the square on the hypotenuse must equal the sum of the squares on the other two sides, in some such manner as this: [Illustration: FIG.
Therefore the square on the hypotenuse must equal the sum of these two squares.
The square on the hypotenuse of a right triangle is equivalent to the sum of the squares on the other two sides.
But QP is the hypotenuse of a triangle PP1Q with a right angle P1.
In every right-angled triangle the square on the hypotenuse is equal to the sum of the squares of the other sides.
The hypotenuse of this triangle would be a right line drawn from Thapsacus to Babylon, which he estimates at 4800 stadia.
Thus, according to his plan, we should have a right-angled triangle, with the right angle next to the frontiers of Carmania, and its hypotenuse less than one of the sides about the right angle!
The first will be the simplest and smallest construction, and its element is that triangle which has its hypotenuse twice the lesser side.
The additional side is determined by the division made in the hypotenuse by dropping a perpendicular line from the apex of the triangle to the hypotenuse.
In this figure the square formed on the hypotenuse is divided into two rectangles.
Here it is demonstrated that a rectangle equivalent to a decagon may have one side equal to the whole hypotenuse and the other equal to half of the perimeter.
In the frame for this, shown below, the squares of the two sides are divided in half by a diagonal line so as to form two triangles and the square of the hypotenuse is divided by two diagonal lines into four triangles.
But all that the reader really requires to know is the Pythagorean law on which many puzzles have been built, that in any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "hypotenuse" in a variety of sentences. We hope that you will now be able to make sentences using this word.
