Geometry: Triangles Classification
 This is a free lesson from our course in Geometry In this lesson you�ll learn the concepts and basics of Classification of Triangles and how to use the properties of particular type for applications. The related contents, explanation with examples are presented by instructor using video and in own hand writing. This will provide the geometry help; in context with triangles and applying the developed skills, for finding solution to real-world problems. The two common systems and basis of triangle classifications are: first by their sides and the second by their angles. For a triangle, you can have all the three sides congruent (equal measure), or two sides congruent, or no side congruent.Congruent sides and congruent angles of triangles are often marked as in the following figures: (More text below video...)
Other useful lessons:
 Triangle Angle-Sum Theorem Triangle Inequality Medians and Midsegment
(Continued from above) Scalene triangle: In a scalene triangle ABC, all the three sides and angles are different from one another (see the figure below). Isosceles triangles: An isosceles triangle has two sides equal in length, called legs or lateral sides and the third side is known as base.   � In an isosceles triangle, the angles opposite the equal sides also measure equal. In the above isosceles ABC, the side AB=AC and ABC = ACB, so ABC is classified as an Isosceles triangle.
Equilateral triangle: In an equilateral triangle, all the sides have the same length. This means that the angles are also equal and hence this form of triangle is also called an equiangular triangle. You know from earlier learning that the sum of the interior angles of any triangle must equal to 180 , therefore, each angle of an equilateral triangle shall be 60 . In the above equilateral ABC, the sides AB = BC = CA and ABC = BCA = CAB = 60 .
Classification by angles:
Acute Triangle: In an acute triangle all the three angles measure less than 90 degrees. E.g. in ABC, all the three i.e. A, C and B are acute angle (Fig- 4).
Right Triangle: In a right triangle, there is one right angle, which measures 90 . This implies that the other two angles will be necessarily acute. In Fig-5 below, the right angle square has been shown and marked as M to show a right angle.
Obtuse Triangle: In an obtuse triangle, one internal angle measures more than 90 . It also implies; other two angles will be acute. In ABC, measure of CBA is more than 90 . (Fig- 6 below). For example, Given: the below triangle, where sides AC=AB and ABC = 65 and ACB = 65 . Classify this triangle and find out measure of angle BAC. You know that the summation of three angles of a triangle equals to 180 . Then BAC = [180 - (65 + 65 )] = 50 .
As both the sides AC = AB, so then ABC is an Isosceles triangle.
m BAC = 50 and the triangle is an Isosceles triangle, is the final answer.
Remember -triangle classification: scalene triangle, isosceles triangle, equilateral triangle acute-angled triangle, obtuse-angled triangle. right-angled triangle.
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