Altitudes, Medians, and Perpendicular Bisectors
MedianA median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the other side.
• The point of concurrency of the medians of a triangle is the centroid of the triangle. |
AltitudeAn altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.
• The point of concurrency of the altitudes of a triangle is the orthocenter of a triangle. Altitudes are used in architecture in bridges to determine whether or not a bridge is sturdy by its height and length. |
Perpendicular BisectorAny point on the perpendicular bisector is equidistant from the endpoints of the given segment. The point at which the perpendicular bisectors of a triangle meet, or the circumcenter, is equidistant from the vertices of the triangle.
Architects often use perpendicular bisectors when creating skyscrapers. They have to know how much land is going to be taken up and which buildings are going to intersect it. |
45°-45°-90° Triangles and 30°-60°-90° Triangles
45°-45°-90° Triangle Theorem states that in a 45°-45°-90° triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times square root of 2.
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30°-60°-90° Triangle Theorem states that in a 30°-60°-90° triangle, the length of the hypotenuse is 2 times the length of the shorter
leg, and the length of the longer leg is the length of the shorter leg times the square root of 3 . This theorem comes into play in architecture when building fences for homes and other buildings. If a fence is rectangular, an architect can cut it into a triangle and use this theorem to measure and figure out the dimensions. |