About Triangle

A triangle is a three-sided polygon. It is one of the basic shapes in geometry. The three angles in a triangle always add up to 180 degrees. Triangle Theorems – Properties Types and FAQs.

Properties of a Triangle

A triangle has three sides and three angles. The angles add up to 180 degrees. The longest side is called the base and the other two sides are called the sides. The angle between the base and a side is called the angle.

Types of Triangle

A triangle is a polygon with three sides and three angles. The three angles are called vertex angles. The sum of the vertex angles is always 180 degrees.

There are three types of triangles:

1. Equilateral Triangle: All three sides are the same length and the three angles are 60 degrees.
2. Isosceles Triangle: Two sides are the same length and the two angles opposite those sides are the same size.
3. Scalene Triangle: No two sides are the same length and the angles are all different sizes.

According to the Measurement of Sides

of a Rectangle (Grade 3), the length of a rectangle is the distance from one corner to the other, and the width is the distance from one side to the other.

Theorems of Triangle

There are six theorems of triangle which are as follows:

Theorem 1: The three angles of a triangle add up to 180°.

Theorem 2: The sum of the squares of the two shorter sides of a triangle is equal to the square of the length of the longest side.

Theorem 3: If a line is drawn from one angle of a triangle to the opposite side, it will intersect the other two angles of the triangle.

Theorem 4: If two lines are drawn from the same angle of a triangle to the two opposite sides, the lines will intersect in a point.

Theorem 5: The altitude of a triangle is the length of the line from the vertex of the triangle to the line of the base that is perpendicular to the base.

Theorem 6: The medians of a triangle are the lines drawn from the vertex of the triangle to the midpoint of the opposite side.

2. Triangle Similarity Theorems

There are three basic similarity theorems for triangles:

The Triangle Sum Theorem states that the sum of the angles in a triangle is 180 degrees.

The Triangle Side Theorem states that the sum of the lengths of the two shorter sides of a triangle is greater than the length of the longest side.

The Triangle Altitude Theorem states that the length of the altitude of a triangle is the shortest distance between the triangle’s opposite vertex and the triangle’s base.

 

3. Basic Proportionality Theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

4. Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

4. Triangle Sum Theorem

The sum of the measures of the angles of a triangle is 180 degrees.

5. Triangle Inequality Theorem

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

Learn Triangle Properties on Vedantu

 

The sum of the angles in a triangle is 180 degrees.

The interior angles of a triangle always sum to 180 degrees.

The exterior angles of a triangle sum to 360 degrees.

Triangle Theorems Explanation

There are three famous triangle theorems:

The Pythagorean theorem: The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

The Law of Cosines: The cosine of the angle between two sides is equal to the product of the length of the sides divided by the length of the cosine of the angle between the sides.

The Law of Sines: The sine of the angle between two sides is equal to the ratio of the length of the opposite side to the length of the hypotenuse.