Geometrical Property of Altitudes
Here we will discuss about a geometrical property of altitudes.
The three altitudes of triangle are concurrent. The point at which they intersect is known as the orthocentre of the triangle.
In the adjoining figure, the three altitudes XP, YQ and ZR intersect at the orthocentre O.
In the adjoining figure ∆XYZ is a right-angled triangle. Here we see that XY ⊥ YZ, YZ ⊥ XY and YM ⊥ XZ.
Thus, the three altitudes XY, YZ and YM intersect at Y. So, Y is the orthocentre of ∆XYZ.
In an obtuse-angled ∆XYZ, the altitudes with respect to XY, YZ and ZX are ZR, XP and YQ respectively.
The altitudes when produced, meet at O. The O is the orthocentre of ∆XYZ.
We see that the orthocentre may lie within, on or outside the triangle.
From Geometrical Property of Altitudes to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Perpendicular Lines | What are Perpendicular Lines in Geometry?|Symbol
Apr 19, 24 02:46 AM
In perpendicular lines when two intersecting lines a and b are said to be perpendicular to each other if one of the angles formed by them is a right angle. In other words, Set Square Set Square If two… -
Fundamental Geometrical Concepts | Point | Line | Properties of Lines
Apr 19, 24 01:55 AM
The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples. -
What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral
Apr 18, 24 02:15 AM
What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments. -
Simple Closed Curves | Types of Closed Curves | Collection of Curves
Apr 18, 24 01:36 AM
In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves. -
Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles
Apr 18, 24 12:31 AM
Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…