By their sides, you can break them down like this: Sides You can classify triangles either by their sides or their angles. A triangle gets its name from its three interior angles. To find the altitude, we first need to know what kind of triangle we are dealing with. To get the altitude for ∠ D \angle D ∠ D, you must extend the side GU 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 DG out very far past the left of the triangle itself. The altitude from ∠ G \angle G ∠ G drops down and is perpendicular to UD, but what about the altitude for ∠ U \angle U ∠ U? Label the sides too side GU=17 cm, UD=37 cm, and DG=21 cm.įor △ G U D \triangle GUD △ 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.
We can construct three different altitudes, one from each vertex.ĭraw a scalene △GUD with ∠G=154°, ∠U=14.8°, and ∠D=11.8°. Here is scalene △ G U D \triangle GUD △ G U D. 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. An 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.
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