Question

What are the properties of all isosceles triangles?

Answer 1

Hint: First, we need to know about the isosceles triangle, which is a triangle that has two equal sides in the length.
The angles are opposite to the given equal sides of the isosceles triangles, in total ${180^0}$.
Triangles are classified into different types on the basis of their sides and angles.

Complete step-by-step solution:

The properties of the isosceles triangle are,
It has two sides of equal length. In the above figure, sides AB and AC are equal in length and can be represented in any of the units like $a$
The angles opposite to equal sides are equal to measure. In the above figure $\angle B,\angle C$ are equal measures.
The altitude from vertex A to the base BC is the perpendicular bisector of the base BC.
The altitude from vertex A to base BC is the bisector of the vertex angle $\angle A$.
The altitude from the vertex divides an isosceles triangle into two congruent right angles triangles. In the above diagram triangles, ADB and ADC are congruent right angles.
The median drawn from vertex A will bisect BC at right angles.
Two isosceles triangles are always similar.
Hence these are the major properties of the isosceles triangle.

Note: Some other properties are given as
In the right angle’s isosceles triangle, the altitude on the hypotenuse is half the length of the hypotenuse.
As isosceles triangle whose two equal sides length is $a$ units and the length of its base is $b$ units.
Then we have $\dfrac{b}{2}\sqrt {{a^2} - \dfrac{{{b^2}}}{4}} $
The perimeter of the isosceles can be calculated using the formula $2a + b$
In the isosceles triangle, the vertical angle is the angle other than the two equal angles (also known as the base angle). The isosceles triangles are always equal in the base angles.
In isosceles triangles, the two bases and one vertical angle are equal to the${180^0}$.
Since in an isosceles triangle, the sides of two sides are equal. Equilateral triangles are all three sides equal.