Every triangle has three altitudes h a , h b and h c , each one associated with one of its three sides. The three altitudes of a triangle or its extensions intersect at a point called orthocenter. The altitude can be inside the triangle , outside it, or even coincide with one of its sides, it depends on the type of triangle it is:. Where is the orthocenter located? The altitude h of the equilateral triangle or the height can be calculated from Pythagorean theorem.
Applying the Pythagorean theorem :. And we obtain that the height h of equilateral triangle is:. Another procedure to calculate its height would be from trigonometric ratios. The altitude h of the isosceles triangle or height can be calculated from Pythagorean theorem. The altitude of a triangle and median are two different line segments drawn in a triangle.
The altitude of a triangle is the perpendicular distance from the base to the opposite vertex. It can be located either outside or inside the triangle depending on the type of triangle. The median of a triangle is the line segment drawn from the vertex to the opposite side that divides a triangle into two equal parts.
It bisects the base of the triangle and always lies inside the triangle. Yes, the altitude of a triangle is a perpendicular line segment drawn from a vertex of a triangle to the base or the side opposite to the vertex. Yes, the altitude of a triangle is also referred to as the height of the triangle. It is denoted by the small letter 'h' and is used to calculate the area of a triangle.
Here, the 'height' is the altitude of the triangle. No, the altitude of an obtuse triangle lies outside the triangle because the angle opposite to the vertex from which the altitude is drawn is an obtuse angle. This is done by extending the base of the given obtuse triangle.
Learn Practice Download. Altitude of a Triangle The altitude of a triangle is a perpendicular that is drawn from the vertex of a triangle to the opposite side. Altitude of a Triangle Definition 2. Altitude of Triangle Properties 3. Altitude of Triangle Formula 4. Difference Between Median and Altitude of Triangle 5. Difference Between Median and Altitude of Triangle.
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Imagine you ran a business making and sending out triangles, and each had to be put in a rectangular cardboard shipping carton. How big a rectangular box would you need?
Your triangle has length, but what is its height? The height or altitude of a triangle depends on which base you use for a measurement. We can construct three different altitudes, one from each vertex. To get that altitude, you need to project a line from side D G out very far past the left of the triangle itself.
Every triangle has three altitudes. Think of building and packing triangles again. You would naturally pick the altitude or height that allowed you to ship your triangle in the smallest rectangular carton, so you could stack a lot on a shelf. What about the other two altitudes? It will have three congruent altitudes, so no matter which direction you put that in a shipping box, it will fit. You only need to know its altitude. The other leg of the right triangle is the altitude of the equilateral triangle, so solve using the Pythagorean Theorem:.
Anytime you can construct an altitude that cuts your original triangle into two right triangles, Pythagoras will do the trick! Use the Pythagorean Theorem for finding all altitudes of all equilateral and isosceles triangles. For right triangles, two of the altitudes of a right triangle are the legs themselves. But what about the third altitude of a right triangle? Use Pythagoras again!
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