How many equal sides on an isosceles triangle

In the figure above, the two equal sides have length and the remaining side has length. This property is equivalent to two angles of the triangle being equal.

An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso same and skelos leg. A triangle with all sides equal is called an equilateral triangle , and a triangle with no sides equal is called a scalene triangle.

An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal. Another special case of an isosceles triangle is the isosceles right triangle.

The height of the isosceles triangle illustrated above can be found from the Pythagorean theorem as. The mean of is given by. Considering the angle at the apex of the triangle and writing instead of , there is a surprisingly simple relationship between the area and vertex angle. As shown in the above diagram, simple trigonometry gives. Erecting similar isosceles triangles on the edges of an initial triangle gives another triangle such that , , and concur.

Is that right? So we have x is equal to 22 degrees in this the first scenario. Now let's think about the second scenario over here. Now we have these two characters are going to be equal to each other because they're both the base angles. So you have 3x plus 5 is equal to x plus Well, you can subtract x from both sides.

And so this becomes 2x plus 5 is equal to We can subtract 5 from both sides and you get 2x is equal to So that is our second scenario. And then we do our third scenario right over here. If this base angle is x plus 16, then this base angle right over here is also going to be x plus They are congruent.

And then we can do the same thing that we did for the first scenario. All of these angles are going to have to add up to degrees. So we have x plus 16 plus x plus 16 plus 3x plus 5. When you add them all together, you're going to get degrees. Now let's add up all the x terms.

So we get 5x. And then you have 16 plus 16 is Plus 37 is equal to degrees. Subtract 37 from both sides, and we get 5x is equal to minus 30 is So that gets us to So it's not going to divide nicely.

You could write it as a mixed number or however else you might want to write it. And we're done. Isosceles triangles are defined as triangles that have two sides of equal length. To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.