Isosceles Triangle: Properties, Perimeter and Area

Isosceles Triangle

What is an isosceles triangle

The isosceles triangle is that triangle that has two sides of equal length. Consequently, the internal angles opposite these sides will be of equal measure.

Note the following figure of the isosceles triangle:

The uneven side is known as the BASE of the isosceles triangle.

Note:

The word «Isosceles» derives from the Greek words:iso(equal) andskelos( leg )

An Isosceles Triangle can have an obtuse angle, a right angle, or three acute angles.

Properties of Isosceles triangle

The isosceles triangle is an important triangle within the classification of triangles, so we will see the most used properties that apply in this geometric figure.

Property 1:

In an isosceles triangle the notable lines: Median, Angle Bisector, Altitude and Perpendicular Bisector that are drawn towards the side of the BASE are equal in segment and length.

See attached figure.

Property 2:

When the remarkable lines of the isosceles triangle are traced, towards the base: Median, Angle Bisector, Altitude and Perpendicular Bisector; these divide the isosceles triangle in to two congruent right triangles.

See attached figure.

In any of these formed right triangles the Pythagorean theorem can be applied to relate the lengths of the sides.

Property 3:

It is very important to know what is accomplished in the following figure:

If it’s true:

AB = BC

Then, when drawing AC, the ABC triangle that is formed will be an isosceles triangle.

Perimeter of Isosceles triangle

Finding the perimeter of the isosceles triangle is very easy to calculate, you only have to know the length of the sides and add them. Remember that in this type of triangle two sides are of equal length, that is very helpful.

See the following figure:

Isosceles triangle ABC:

The length of the sides are: AB = BC = a; AC = b

Then the perimeter of the isosceles triangle will have the following formula:

∴ Perimeter of Isosceles Triangle = 2a + b

Area of Isosceles triangle

The area of the isosceles triangle is calculated by knowing the base and its height, then the formula is applied to find the area of every triangle:

Area = [Base x Height]/2

See the following figure:

Of the isosceles triangle ABC:

«h»: length of height

«b»: length of base

The formula for finding the area of the isosceles triangle will be:

∴ Area of Isosceles Triangle = b.h/2