![]() We’ll also answer some common questions about triangles and what type of angles they can have.Ī triangle is a polygon that always has exactly three sides and three angles. In this article, we’ll take a closer look at triangles and their angles. For example, the largest angle of a triangle will be across from its longest side. Of course, comparing the angles of triangles can also tell us about the sides. ![]() Equilateral triangles have three sides (and angles) that are the same. Isosceles triangles have two sides (and angles) that are the same. A triangle has either two or three acute angles. Triangles can have at most one right or obtuse angle. We can use their angles to categorize triangles and make statements about what they look like and how their sides are related.Ī triangle’s angles sum to 180 degrees. In this case, the sets overlap.Triangles come up often in mathematics, and for good reason – they are useful for a variety of purposes. You may find the other possible triangles as part of an assignment or exploration:Ī more advanced way of thinking of the relationships between types of triangles is with a Venn diagram (This could be used in presenting material to intermediate grades students, and of exploring with middle grades students) ![]() I found an isosceles right triangle, and I have entered it in a table to find all of the possible combinations. For example: can you have an isosceles right triangle? Try it with this applet, and see if you find one that works (remember, to be isosceles, two sides must be the same length, and to be right, one angle must be 90°).įinding all of the ways that you can and can't combine an angle and a side length property is an appropriate task for encouraging students to do higher level thinking, and can be done as early as third grade if students have appropriate concrete manipulative tools to help them experiment with triangles. Practice problem-how are right, acute and obtuse triangles related?Ī good exercise for beginning to think at the analysis level (Van Hiele level 2) is to consider when a triangle can have both a side length and an angle property. Isosceles and Scalene triangles are disjoint sets-they don't overlap at all because a triangle can never be both isosceles and scalene. If you have no sides the same length, however, you can never have two sides the same length, so we can show the relationships between equilateral, isosceles and scalene triangles this way:Įquilateral triangles are a subset of isosceles triangles, because every equilateral triangle is also isosceles (though some isosecles triangles are equilateral and some are not). Notice that if you have all 3 sides the same length, you automatically have at least 2 sides the same length. Obtuse triangles have one angle that measures more than 90° Right triangles have one angle that is equal to 90°Īcute triangles have all 3 angles less than 90° The second 3 are defined by angle properties: Isosceles triangles have at least 2 sides the sameĮquilateral triangles have all 3 sides the same Scalene triangles have all 3 sides different lengths The first 3 are usually defined by side length properties: There are 6 special named types of triangles: scalene triangles, isosceles triangles, equilateral triangles, right triangles, acute triangles, and obtuse triangles. ![]() Most of this work with triangles is appropriate for students grades 3 and above. This set of problems shows the sorts of thinking we want students to develop to be ready for High school math. This discussion is aimed at a Van Hiele level 1-2 understanding, and thus is fairly sophisticated for elementary students.
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