In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite...

if the circumcenter is located outside the triangle, then the triangle is obtuse. An altitude of a triangle is a straight line through a vertex and perpendicular...

geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line...

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...

of a triangle, usually denoted by H, is the point where the three (possibly extended) altitudes intersect. The orthocenter lies inside the triangle if and...

derived from the formula of an isosceles triangle by Pythagoras theorem: the altitude h {\displaystyle h} of a triangle is the square root of the difference...

point of the triangle's three altitudes, each of which perpendicularly connects a side to the opposite vertex. In the case of an acute triangle, all three...

triangle and forming the altitude of the triangle. Two small constellations, Sagitta and Vulpecula, lie between Aquila in the south of the triangle and...

that the altitude bisects the base and partitions the isosceles triangle into two congruent right triangles. The Euler line of any triangle goes through...

T=bh/2,} where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height"...

}}={\frac {\sqrt {4a^{2}b^{2}-(a^{2}+b^{2}-c^{2})^{2}}}{2ab}}.} The altitude of the triangle on base ⁠ a {\displaystyle a} ⁠ has length ⁠ b sin ⁡ γ {\displaystyle...

triangles have bases of equal length and share a common altitude from the (extended) base, and a triangle's area equals one-half its base times its height. We...

triangle ABC with side length 2 and with point M as the midpoint of segment BC. Draw an altitude line from A to M. Then ABM is a 30°–60°–90° triangle...

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length...

incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent...

coordinate system Altitude (triangle), in geometry, a line passing through one vertex of a triangle and perpendicular to the opposite side Altitude (ALT album)...

then the altitude dropped perpendicularly from the apex to the base intersects the extended base outside of the triangle. The area of a triangle is its...

Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. Heronian triangles are named...

the geometric shape. Triangle Acute and obtuse triangles Altitude (triangle) Area bisector of a triangle Angle bisector of a triangle Angle bisector theorem...

parts d and e. The new triangle, ACH, is similar to triangle ABC, because they both have a right angle (by definition of the altitude), and they share the...

any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. It is a theorem commonly employed in various math...

not an altitude of triangle △ABC. Let B1 be the base (foot) of the altitude in the triangle △ABD through B and let C1 be the base of the altitude in the...

the triangle The foot of each altitude The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet;...

trigonometric functions of those angles, the area of the triangle, the medians of the sides, the altitudes, the lengths of the internal angle bisectors from...

Black triangles are UFOs reported as having a triangular shape and dark color, typically observed at night, described as large, silent, hovering, moving...

In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example,...

the orthic triangle (whose vertices are at the feet of the altitudes of the reference triangle).: p. 447 : p. 102  The tangential triangle is homothetic...

triangles). Corresponding altitudes of similar triangles have the same ratio as the corresponding sides. Two right triangles are similar if the hypotenuse...

denote both the triangle's vertices and the angle measures at those vertices; H is the orthocenter (the intersection of the triangle's altitudes); D, E, F are...

definitions. These include: The height or altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;...