Today we’re going to take a look at a shape that appears extremely often on the geometry portion of your test: the isosceles triangle. Since geometry boils down to circles and triangles (and the lines and curves that define them), understanding this very common triangle type is essential. Take a look at this image which shows the essentials of an isosceles triangle:
An isosceles triangle is one where at least two of the sides are equal in length. The specific case where all three sides are equal in length is an equilateral triangle and the implications of that are more widely known, so we’ll reserve our current discussion to the case where two sides are equal in length and the third is different.
The reason that isosceles triangles are so widely used is that they allow you to infer a large amount of information from a relatively small number of given facts. For instance, in the figure above if we’re told that angle A measures 36 degrees, we can solve for the measures of both angles B and C. Since the length of sides AC and AB are equal, the measures of angles B and C must also be equal. So, solving for the measure is simply this:
36 + 2(AB) = 180
Another great thing about isosceles triangles is that it works both ways. If rather than knowing anything about the sides, we knew that angles B and C were equal in measure we would still be able to infer that sides AC and AB were equal. That gives lots of flexibility to the test maker. He can present you with the sides or the angles and rely on you to get the rest of the information.
The last great thing to know about isosceles triangles is that they have a line of symmetry that bisects the non-equal angle and creates two right triangles. See the figure below:
So, not only do isosceles triangles have their own unique and helpful properties, but they can easily be turned into right triangles which are extremely helpful as well. Keep these ideas in mind as you work through the geometry section of your next test!