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The altitude from A (dashed line segment) intersects the extended base at D (a point outside the triangle). 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 the apex.
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 legs of a right triangle are perpendicular to each other. The altitudes of a triangle are perpendicular to their respective bases. 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 term "base" denotes any side, and "height" denotes the length of a perpendicular from the vertex opposite the base onto the line containing the base. Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book Elements in 300 BCE. [1]
The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the height. The area of a triangle equals one-half the product of height and base length.
Let ABC be an equilateral triangle whose height is h and whose side is a. Let P be any point inside the triangle, and s, t, u the perpendicular distances of P from the sides. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA.
This formula can be derived by partitioning the n-sided polygon into n congruent isosceles triangles, and then noting that the apothem is the height of each triangle, and that the area of a triangle equals half the base times the height. The following formulations are all equivalent:
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its