Examples: Properties of Isosceles Triangles
Math
Using the Properties of Isosceles Triangles
Welcome to examples of using the properties of isosceles triangles to determine information about a triangle. Here's our first example, notices triangle is an isosceles triangle because it has at least two congruent sides. This side here is congruent to this side here. We also need to remember from the isosceles triangle theorem that the angles that are opposite these two congruent sides are congruent as well. So this angle here is congruent to this angle here. So we need to take this information and determine the value of X and determine the value of Y let's start by determining the value of X if these two sides are congruent, then the same length, so four X plus three must equal two X plus 29.
So now we have an equation that we can solve for X let's go ahead and subtract two X on both sides. This will give us two X plus three equals 29, now we'll subtract three on both sides. And now we have two X equals 26, so we can divide both sides by two. So X is equal to 13. That takes care of X now and see if we can determine the value of Y since we already determined that these two angles that are opposite the congruent sides must also be congruent. We know that three Y plus 2° must equal 41°, so to set up our equation will have three Y plus two equals 41. And now we can solve this equation for Y so we'll subtract two on both sides. And I'll give us three Y equals 39. And now we divide both sides by three. And 39 divided by three is equal to 13. So using the properties of isosceles triangles, we're able to determine the value of X and the value of Y let's take a look at one more example. Again, here we have an isosceles triangle because we have two congruent sides. So why do we know that the angles that are opposite these congruent sides are also congruent. So this angle here is congruent to this angle here.
So we know these angles are congruent or have the same measure, but we also have to remember that the sum of the interior angles of this triangle would be 180°. So we can take the total sum of the interior angles, and subtract out this angle that measures 28°, and that will give us the sum of the two base angles, which we know are congruent. So this is going to give us 152° for the sum of these two angles. And since it congruent, we can just divide this by two, and that will tell us the measure of each base angle. So each of these base angles has a measure of 76°. So now we can determine the value of X, our equation is going to be 5 X plus one is going to equal 76. So we'll subtract one on both sides. And now divide by 5. So we have X equals 15. So again, we're able to determine the value of X by using the properties of an isosceles triangle, as well as the the triangle sum theorem. I hope you found these two examples helpful.