104 LearnersLast updated on August 13th, 2025
Properties of Triangle
A triangle is a type of polygon that has unique properties. These properties help students simplify geometric problems related to triangles. The properties of a triangle include having three sides and three angles, the sum of which is always 180 degrees. These properties help students to analyze and solve problems related to symmetry, angles, and area. Now let us learn more about the properties of a triangle.
What are the Properties of a Triangle?
The properties of a triangle are fundamental and help students understand and work with this type of polygon. These properties are derived from the principles of geometry. There are several properties of a triangle, and some of them are mentioned below: Property 1: Sum of Angles The sum of the interior angles in a triangle is always 180 degrees. Property 2: Types Based on Sides Triangles can be classified as equilateral, isosceles, or scalene based on their side lengths. Property 3: Types Based on Angles Triangles can also be classified as acute, right, or obtuse based on their angles. Property 4: Pythagorean Theorem In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Property 5: Area Formula The formula used to calculate the area of a triangle is given below: Area = ½ x base x height
Tips and Tricks for Properties of a Triangle
Students tend to confuse and make mistakes while learning the properties of triangles. To avoid such confusion, we can follow the following tips and tricks: Sum of Angles is 180 Degrees: Students should remember that the sum of the three interior angles in any triangle is always 180 degrees. Pythagorean Theorem for Right Triangles: Students should remember that in a right triangle, the Pythagorean theorem can be applied to find missing side lengths. Classifying Triangles by Angles and Sides: Students should practice identifying triangles as equilateral, isosceles, or scalene and as acute, right, or obtuse.
Confusing Different Types of Triangles
Students should remember that equilateral triangles have all sides equal, isosceles have two equal sides, and scalene have no equal sides.
Mistake 1
Misinterpreting the Angle Sum Property
Students should know and remember that the sum of the angles in any triangle is always 180 degrees.
Mistake 2
Incorrectly Applying the Area Formula
Students should practice using the formula to find the area of a triangle, which is given below. The students must also understand the representations of base and height. Area = ½ x base x height
Mistake 3
Misunderstanding the Pythagorean Theorem
Students should remember that the Pythagorean theorem applies only to right triangles and involves the relationship between the sides.
Mistake 4
Forgetting the Triangle Inequality Theorem
Students must remember that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Mistake 5
Solved Examples on the Properties of Triangles
In a triangle, the three corners are marked as A, B, and C. If AB = 5 cm, BC = 7 cm, and AC = 5 cm, what type of triangle is it?
The triangle is isosceles.
Problem 1
In a triangle, if two sides are equal, it is classified as an isosceles triangle. Since AB = 5 cm and AC = 5 cm, the triangle is isosceles.
In a triangle ABC, the angle ABC = 60 degrees, and angle ACB = 60 degrees. What is the measure of angle BAC?
Explanation
Angle BAC = 60 degrees.
Problem 2
In a triangle, the sum of the angles is 180 degrees. Here, angle ABC + angle ACB + angle BAC = 180 degrees. Thus, 60 + 60 + angle BAC = 180. Hence, angle BAC = 60 degrees.
In a right triangle, if one leg measures 6 cm and the other leg measures 8 cm, what is the length of the hypotenuse?
Explanation
The hypotenuse is 10 cm.
Problem 3
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Thus, hypotenuse² = 6² + 8² = 36 + 64 = 100. Hence, hypotenuse = √100 = 10 cm.
In triangle ABC, if angle A is 90 degrees, and angle B is 45 degrees, what is the measure of angle C?
Explanation
Angle C = 45 degrees.
Problem 4
Since the sum of angles in a triangle is 180 degrees, angle C = 180 - (angle A + angle B) = 180 - (90 + 45) = 45 degrees.
A triangle has a base of 12 cm and a height of 5 cm. What is the area of the triangle?
Explanation
Area = 30 square cm.
A triangle is a polygon with three sides and three angles.
1.How many sides does a triangle have?
2.Are all angles in a triangle equal?
3.How do you find the area of a triangle?
4.Can a triangle have all right angles?
Common Mistakes and How to Avoid Them in Properties of Triangles
Students tend to get confused when understanding the properties of triangles, and they tend to make mistakes while solving problems related to these properties. Here are some common mistakes students tend to make and the solutions to said common mistakes.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
