Types of triangle and their properties

Non-examples of Triangles The above figures are non-examples of triangles. These • The first figure is four-sided. • The second figure is an open shape. • The third figure has a curved side. Parts of a Triangle • A triangle has 3 sides. In triangle ABC, the sides are AB, BC, and CA. • The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠. A triangle has three angles. The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively. • The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C. Properties of a Triangle • The sum of all three interior angles of a triangle is always equal to 180⁰. • The sum of the length of any two sides of a triangle is always greater than the length of the third side. • The area of a triangle is equal to half of the product of its base and height. Types of Triangles Triangles can be classified based on the length of the sides or their angle measurements. To classify triangles according to their angles, we measure each of their interior angles. Triangles can be classified by angles, as: • • • The • • • To classify triangles according to both angles and sides, we measure the interior angles and length of the sides of the triangle. Triangles classified based on both angles and sides are – • Acute Equilateral Triangle • Right Isosceles Triangle • O...

Classification by sides (length of their sides) In an equilateral triangle, all the sides are congruent. That is, all three sides of the triangle are equal. Since all the sides are equal, all the interior angles will also be equal. To find the measure of each angle, an important property of a triangle is to be recalled. ‘The sum of the angles of a triangle is 180 degrees’. Thus dividing 180 to three equal parts, it’s 60. Each angle of an equilateral triangle is 60 degrees. Therefore, an equilateral triangle is also known as an equiangular triangle. In an isosceles triangle, only two sides are equal. If two sides are equal, then their angles will also be equal. Thus, the angles opposite to the equal sides are equal. By now, you should have guessed it right. A scalene triangle is a triangle in which all three sides are unequal. Thus all three angles are different. In other words, no two angles are equal in a scalene triangle. Classification by angles (interior angles) In an acute triangle, all three interior angles are acute. An acute angle is an angle less than 90 degrees. It also means that all three angles of an acute triangle are less than 90 degrees. In an obtuse triangle, one angle of the triangle is always greater than 90 degrees, which is called obtuse. Thus a triangle in which one of the angles measures more than 90 is an obtuse triangle. In a right triangle, one angle is always equal to 90 degrees. The representation of this triangle is shown below. The side opposi...

Keta Bhakta Keta Bhakta graduated from University of Minnesota with a B.S. in Neuroscience and then with a D.D.S. as a dentist. She has tutored many students in various math and science subjects. She began working as a professor at the University of Minnesota School of Dentistry in 2013. • Instructor Triangle Art In this activity, students will be creating a work of art that has each of the types of triangles described in the lesson. For example, students might create a scene with a house that has an equilateral triangle for the roof and a right triangle for the side of a shed. They could use scalene triangles for the wings of some birds in the distance, or isosceles triangles to create a small camp fire in the backyard. Students can create their art using traditional art supplies or with a program like Google Drawings. Directions In this activity you're going to be combining your artistic skills with your knowledge of different types of triangles. You will be creating a work of art that has at least one of each type of triangle you learned about in the lesson: • Equilateral • Right • Isosceles • Scalene • Acute • Obtuse Your art can be of any subject matter, such as a landscape, a still life, or even a self portrait. You can create your art digitally or with art supplies, such as markers, colored pencils, paint or even by creating a collage. You should also include a description of where each of the types of triangles are in your art. To make sure your art meets the crite...

Classifying Triangles Classification of triangles is done according to the length of their sides and the measure of the angles. A triangle is a simple polygon with 3 sides, 3 interior angles, and 3 vertices that are joined with each other and it is denoted by the symbol △. This is the most common shape seen in math and nature and is of various types. In this article, classifying triangles is seen in detail along with a few solved examples to understand the concept better. 1. 2. 3. 4. 5. Classification of Triangles Classification of triangles is done based on their sides and angles. In other words, the characteristics of a triangle's size and shape help in distinguishing the type of triangle. The table below shows the different types of triangles based on their angles and sides. Based on Sides Based on Angles Based on Sides & Angles Equilateral Triangle Acute Angle Equiangular Triangle Isosceles Triangle Obtuse Angle Isosceles Right Triangle Scalene Triangle Right Angle Obtuse Isosceles Triangle Acute Isosceles Triangle Right Scalene Triangle Obtuse Scalene Triangle Acute Scalene Triangle Let us see each type in detail. Classification of Triangles Based on Sides A triangle consists of three sides but the factor to classify them is the length of the sides. It is specifically based on the ratio of the lengths of the sides with one another rather than the unit measure. Hence, triangles are classified on the number of sides with the same length equal to each other or not equal ...

All Subjects • Fundamental Ideas • • • • • • • • Parallel Lines • • • • • Triangles • • • • • • • • • • • Polygons • • • • • • • • Perimeter and Area • • • • • • • • Similarity • • • • • • • • Right Angles • • • • • • Circles • • • • • • • • • Geometric Solids • • • • • • • • Coordinate Geometry • • • • • • • Classifying Triangles by Sides or Angles Triangles can be classified either according to their sides or according to their angles. All of each may be of different or the same sizes; any two sides or angles may be of the same size; there may be one distinctive angle. The types of triangles classified by their sides are the following: • Equilateral triangle: A triangle with all three sides equal in measure. In Figure 1, the slash marks indicate equal measure. Figure 1 Equilateral triangle • Isosceles triangle: A triangle in which at least two sides have equal measure (Figure 2). Figure 2 Isosceles triangles • Scalene triangle: A triangle with all three sides of different measures (Figure 3). Figure 3 Scalene triangle The types of triangles classified by their angles include the following: • Right triangle: A triangle that has a right angle in its interior (Figure 4). Figure 4 Right triangle • Obtuse triangle: A triangle having an obtuse angle (greater than 90° but less than 180°) in its interior. Figure 5 shows an obtuse triangle. Figure 5 Obtuse triangle • Acute triangle: A triangle having all acute angles (less than 90°) in its interior (Figure 6). Figure 6 Acute tria...