Triangle Study Guide

Definition

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Types of Triangles

There are several types of triangles based on their sides and angles:

• Equilateral Triangle: A triangle with all three sides of equal length and all three angles are equal to 60 degrees.
• Isosceles Triangle: A triangle with at least two sides of equal length and the two corresponding angles are equal.
• Scalene Triangle: A triangle with all three sides of different lengths and all three angles are different.
• Right Triangle: A triangle with one 90-degree angle.
• Acute Triangle: A triangle with all angles less than 90 degrees.
• Obtuse Triangle: A triangle with one angle greater than 90 degrees.

Properties

Some important properties of triangles include:

• Interior Angles: The sum of the interior angles of a triangle is always 180 degrees.
• Exterior Angles: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
• Pythagorean Theorem: In a right-angled 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.

Formulas

Some common formulas related to triangles are:

• Area of a Triangle: A = (1/2) * base * height
• Perimeter of a Triangle: P = a + b + c, where a, b, and c are the lengths of the three sides.
• Heron's Formula: A = sqrt(s * (s - a) * (s - b) * (s - c)), where A is the area of the triangle and s is the semi-perimeter, (a+b+c)/2.

Practice Problems

Here are some practice problems to test your understanding:

1. Find the area of a triangle with base = 6 cm and height = 8 cm.
2. Determine whether the following triangle is a right triangle: side lengths are 3 cm, 4 cm, and 5 cm.
3. Classify the triangle with angles measuring 60°, 60°, and 60°.

Remember to use the properties and formulas of triangles to solve these problems.