![]() Now that you have worked through this lesson, you are able to recognize and name the different types of triangles based on their sides and angles. For right triangles, two of the altitudes are the legs and the third altitude is inside the triangle.For oblique, obtuse triangles: the altitude dropped from the obtuse angle will be inside the triangle and the other two altitudes will fall outside the triangle.For oblique, acute triangles: the altitudes will always be inside the triangle. ![]() Since every triangle can be classified by its sides or angles, try focusing on the angles: Where to look for altitudes depends on the classification of triangle. Here is right △ R Y T, helpfully drawn with the hypotenuse stretching horizontally.Ĭan you see how constructing an altitude from ∠ R down to side Y T will divide the original, big right triangle into two smaller right triangles? Use Pythagoras again! Where to Look for the Altitude But what about the third altitude of a right triangle? The other leg of the right triangle is the altitude of the equilateral triangle, so solve using the Pythagorean Theorem:Īnytime 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.įor right triangles, two of the altitudes of a right triangle are the legs themselves. You only need to know its altitude.Ĭonstructing an altitude from any base divides the equilateral triangle into two right triangles, each one of which has a hypotenuse equal to the original equilateral triangle's side, and a leg ½ that length. It will have three congruent altitudes, so no matter which direction you put that in a shipping box, it will fit. What about an equilateral triangle, with three congruent sides and three congruent angles, as with △ E Q U below? Not every triangle is as fussy as a scalene, obtuse triangle. What about the other two altitudes? If you insisted on using side G U ( ∠ D) for the altitude, you would need a box 9.37 c m tall, and if you rotated the triangle to use side D G ( ∠ U), your altitude there is 7.56 c m tall. 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.Īltitude for side U D ( ∠ G) is only 4.3 c m. Think of building and packing triangles again. 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.
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