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Think of building and packing triangles again.
#EFINE ALTITUDE GEOMETRY HOW TO#
How to Find the Altitude of a TriangleĮvery triangle has three altitudes. To get the altitude for ∠ D, you must extend the side G U far past the triangle and construct the altitude far to the right of the triangle. To get that altitude, you need to project a line from side D G out very far past the left of the triangle itself. The altitude from ∠ G drops down and is perpendicular to U D, but what about the altitude for ∠ U? We can construct three different altitudes, one from each vertex.įor △ G U D, no two sides are equal and one angle is greater than 90 °, so you know you have a scalene, obtuse (oblique) triangle. The height or altitude of a triangle depends on which base you use for a measurement. How big a rectangular box would you need? Your triangle has length, but what is its height? Imagine you ran a business making and sending out triangles, and each had to be put in a rectangular cardboard shipping carton. Obtuse triangles - One interior angle is obtuse, or greater than 90 °Īn altitude is a line drawn from a triangle's vertex down to the opposite base, so that the constructed line is perpendicular to the base.Acute triangles - All interior angles are acute, or each less than 90 °.Oblique triangles break down into two types: Right - One right angle ( 90 °) and two acute angles.Anglesīy their interior angles, triangles have other classifications:
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Most mathematicians agree that the classic equilateral triangle can also be considered an isosceles triangle, because an equilateral triangle has two congruent sides.
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It is listed below, but appears on a separate page along with historical remarks. The earliest known proof was given by William Chapple (1718-1781). The timing of the first proof is still an open question it is believed, though, that even the great Gauss saw it necessary to prove the fact. This is a matter of real wonderment that the fact of the concurrency of altitudes is not mentioned in either Euclid's Elements or subsequent writings of the Greek scholars.