Properties of Triangle – types & formulas

The basic properties of a triangle and its types are:

properties

1. A triangle has three sides, three angles, and three vertices.

2. The sum of all the interior angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

3. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

4. The side opposite the largest angle of a triangle is the largest side.

5. Any exterior angle of the triangle is equal to the sum of its opposite interior angles. This is called the exterior angle property of a triangle.

types of triangles:

Based on the angle: Acute Angle Triangle, Oblique Angle Triangle, Right Angle Triangle.

based on its sides: Equilateral triangle, Scalene triangle, Isosceles triangle

.

prepare some of the unknown things:

perimeter: it is found in a similar or equal way for any type of triangle by adding the length of its three sides

area: for any triangle we find the area by multiplying its base times the height divided by two ((b*h)/2)

to find an angle in a right triangle: we use the trigonometric ratios (sine, cosine, tangent and their inverses)

to find an angle of a non-right triangle: we use the law of sines or the law of cosines

to find a side of a right triangle: we use the Pythagorean theorem (a^2+b^2=c^2)

to find a side of a non-right triangle: we use the law of sines or cosines

an acute angle triangle: is a triangle that has all 3 angles less than 90°

an obtuse-angled triangle: is a triangle that has an angle that measures more than 90°.

a scalene triangle: is a triangle that has three sides of different lengths.

an isosceles triangle.: is a triangle that has two sides of the same length and the third side of different length length.

an equilateral triangle: is a triangle that has all three sides of the same length.

a right triangle: is a triangle that has one angle that measures exactly 90°.

Special Cases of Right Triangles

45-45-90 triangle, in this triangle:

- Two angles measure 45° and the third angle is a right angle.

- The sides of this triangle will be in the ratio – 1:1:√2 respectively.

- This is also called an isosceles right triangle since two angles are equal.

30-60-90 triangle, In this triangle:

- This is a right triangle, since one angle = 90°

- The angles of this triangle are in the ratio - 1: 2: 3, and

- The sides opposite these angles will be in the ratio – 1: √3: 2 respectively

- This is a scalene right triangle since all three angles are different.

Triangle Properties

Properties of Triangle – types & formulas [Video & Practice]. (2022, 19 octubre). e-GMAT Blog | Best GMAT blog on the planet. https://e-gmat.com/blogs/properties-of-triangles/