A 2D figure having three sides in the artesian plane is known as a trigon or popularly known as a triangle. Based on the sides, the triangle is divided into three types: Equilateral triangle, Isosceles triangle, and scalene triangle.
The main purpose of this article is to define various properties of the isosceles triangle. Let us learn about the triangle in detail as we unravel its properties.
Suppose we have a triangle PQR which is an isosceles triangle; the isosceles triangle theorem states that the angles opposite to two equal sides are equal and congruent if those lengths (sides) of a triangle are also congruent.
The Converse of the theorem is also true, which states that two sides of an isosceles triangle are congruent if the corresponding angles opposite to those lengths are equal or congruent. Therefore, we can conclude that ∠PQR = ∠PRQ and PQ = PR in the figure given above. We can prove this by drawing a perpendicular from vertex P. In an isosceles triangle, any perpendicular drawn from the vertex opposite to the base bisects the base. Therefore, let us mark the point where the perpendicular bisects the base QR as O. We can see that angle POQ and POR are 90 degrees in value (due to the perpendicular PO). Since the base is split into two halves, QO = OR. Angle PQO is also equal to angle PRO (angles of an isosceles triangle). Hence, due to the Angle Side Angle congruence rule, the triangles POQ and POR are congruent to each other. Therefore, side QP is congruent to side PR, which proves the theorem.
You may also want to learn about the Area of Triangle Formula.
Below are listed all the important properties related to an isosceles triangle. They are: