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A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
The perpendicular bisectors of the sides also play a prominent role in triangle geometry. The Euler line of an isosceles triangle is perpendicular to the triangle's base. The Droz-Farny line theorem concerns a property of two perpendicular lines intersecting at a triangle's orthocenter.
These include the Calabi triangle (a triangle with three congruent inscribed squares), [10] the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), [11] the 80-80-20 triangle appearing in the Langley's Adventitious Angles puzzle, [12] and the 30-30-120 triangle of the triakis triangular tiling.
The Tarry point of a triangle is the point of concurrency of the lines through the vertices of the triangle perpendicular to the corresponding sides of the triangle's first Brocard triangle. The Schiffler point of a triangle is the point of concurrence of the Euler lines of four triangles: the triangle in question, and the three triangles that ...
SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure. ASA: Two interior angles and the side between them in a triangle have the same measure and length, respectively, as those in the other triangle. (This is the basis of surveying by triangulation.)
Thus, the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometric functions. In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that
Two orthologic triangles In geometry , two triangles are said to be orthologic if the perpendiculars from the vertices of one of them to the corresponding sides of the other are concurrent (i.e., they intersect at a single point ).
Dissecting the right triangle along its altitude h yields two similar triangles, which can be augmented and arranged in two alternative ways into a larger right triangle with perpendicular sides of lengths p + h and q + h. One such arrangement requires a square of area h 2 to complete it, the other a rectangle of area pq. Since both ...