Mathematics is Fun

ISOSCELES TRIANGLE

BY

Yulianti

20402110103

DEPARTMENT OF MATHEMATICS EDUCATION (5 & 6)

FACULTY OF TARBIYAH

ISLAMIC STATE UNIVERSITY ALAUDDIN MACASSAR

Isosceles Triangle

If two of the sides of a triangle are of equal size the triangle is isosceles triangle.

                                                                          C

AB

Properties of Isosceles Triangle

1.      The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle.

2.      The base angles of an isosceles triangle are always equal. In the figure above, the angles ∠ABC and ∠ACB are always the same

3.      When the 3rd angle is a right angle, it is called a "right isosceles triangle".

4.      The altitude is a perpendicular distance from the base to the topmost vertex.

The height or altitude of the isosceles triangle illustrated above can be found from the Pythagorean theorem as

Where

h = the altitude

b = the lenght of the leg

a = the base

To find the base given the leg and altitude, use the formula :

where :

b = the lenght of a leg

h = the altitude

To find the leg length given the base and altitude, use the formula:

Where :

h = the altitude

a= the base

The area is therefore given by

 

 

 

The circumference of the isosceles tringle is

Where

 a = base

b = leg

interior angles

If you are given one interior angle of an isosceles triangle you can find the other two.

For example,

  We are given the angle at the apex as shown on the right of 40°. We know that the interior angles of all triangles add to 180°. So the two base angles must add up to 180-40, or 140°. Since the two base angles are congruent (same measure), they are each 70°.

If we are given a base angle of say 45°, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180°. So the apex angle must be 180-45-45 or 90°.