Triangle Study Guide

Definition:

A triangle is a closed two-dimensional shape with three straight sides and three angles.

Types of Triangles:

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

• Equilateral Triangle: A triangle with all three sides of the same length and all three angles are equal (60 degrees).
• Isosceles Triangle: A triangle with two sides of the same length and two equal angles.
• Scalene Triangle: A triangle with all three sides of different lengths and no equal angles.
• Right Triangle: A triangle with one right angle (90 degrees).
• Acute Triangle: A triangle with all three angles less than 90 degrees.
• Obtuse Triangle: A triangle with one angle greater than 90 degrees.

Properties of Triangles:

Triangles have several important properties:

• Sum of Angles: The sum of the three interior angles of a triangle is always 180 degrees.
• Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
• Area: The area of a triangle can be calculated using the formula: Area = (1/2) * base * height.
• Perimeter: The perimeter of a triangle is the sum of the lengths of its three sides.

Triangle Inequality Theorem:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Practice Problems:

Now that you've learned about triangles, here are some practice problems to test your understanding:

1. Calculate the area of a triangle with a base of 8 cm and a height of 5 cm.
2. Determine the type of triangle with side lengths of 6 cm, 8 cm, and 10 cm.
3. Find the missing angle in a triangle with angles of 45 degrees and 60 degrees.