Scalene Triangle

A scalene triangle is a type of triangle that has three sides of different lengths. In other words, all the three sides of a scalene triangle are unequal, and all the three angles are also different from each other.

To identify a scalene triangle, you can look for the following characteristics:

Three unequal side lengths
Three different interior angles

Properties of a Scalene Triangle:

Each interior angle measures less than 180 degrees
No two sides are equal in length
No two angles are equal in measure

Formulas and Concepts:

Perimeter of a Scalene Triangle:

The perimeter of a scalene triangle is found by adding the lengths of all three sides together.

Perimeter = Side1 + Side2 + Side3

Area of a Scalene Triangle:

To calculate the area of a scalene triangle, you can use Heron's formula, which is based on the semi-perimeter of the triangle (s) and the lengths of its three sides (a, b, c).

Area = √[s(s - a)(s - b)(s - c)], where s = (a + b + c) / 2

Examples of Scalene Triangles:

Here are some examples of scalene triangles:

Triangle ABC: with side lengths AB = 5 units, BC = 7 units, and AC = 9 units
Triangle PQR: with side lengths PQ = 8 cm, QR = 10 cm, and PR = 12 cm

Properties and Characteristics:

Since all the sides and angles of a scalene triangle are different, it does not have any lines of symmetry or rotational symmetry. It is also not a right-angled triangle, as it does not have a right angle (90 degrees).

Practice Problems:

1. Calculate the perimeter and area of a scalene triangle with side lengths 6 cm, 8 cm, and 10 cm.

2. Determine whether the following triangle is scalene or not, given the side lengths: AB = 3 units, BC = 4 units, and AC = 5 units.

Understanding the concept of scalene triangles is important in geometry and can help in solving various problems related to triangles and their properties.

Now that you have a good understanding of scalene triangles, you can practice solving problems and identifying them in different geometric figures.

Happy studying!

◂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.