Triangle Study Guide

What is a Triangle?

A triangle is a closed, three-sided polygon. The sum of the interior angles of a triangle is always 180 degrees.

Types of Triangles

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

Equilateral Triangle: All three sides are of equal length, and all three angles are of equal measure (60 degrees).
Isosceles Triangle: Two sides are of equal length, and the two angles opposite those sides are of equal measure.
Scalene Triangle: All three sides have different lengths, and all three angles have different measures.
Right Triangle: One of the angles is a right angle (90 degrees).
Acute Triangle: All three angles are less than 90 degrees.
Obtuse Triangle: One of the angles is greater than 90 degrees.

Triangle Formulas

Here are some important formulas related to triangles:

Perimeter: The perimeter of a triangle is the sum of the lengths of its three sides: P = a + b + c
Area: The area of a triangle can be calculated using the formula: A = (1/2) * base * height
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: c^2 = a^2 + b^2

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. In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds: a + b > c

Geometric Properties

Triangles also have several geometric properties, such as the altitude, median, and centroid, which are important for solving various problems.

Practice Problems

Now that you've learned about triangles, try solving the following practice problems:

Find the area of a triangle with a base of 6 units and a height of 8 units.
Determine the type of triangle with side lengths of 5, 5, and 5 units.
If one angle of a triangle is 45 degrees, and another angle is 60 degrees, what is the measure of the third angle?

Good luck with your triangle studies!

◂Math Worksheets and Study Guides Eighth Grade. Perimeter and area

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.