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Properties of Triangles: Practice Questions (Part-2).

GMAT Geometry Concepts and Formulas on Triangles (Part-1).

If you liked this article, you may also like to read the following advanced level articles on triangles

The height of a triangle is equal to the length of the perpendicular dropped from a vertex to its opposite side, and this side is considered the base.

In the case of a right-angled triangle, this side is called the hypotenuse.

Similarly, the side opposite to the largest interior angle is the longest side and vice versa.

The side opposite to the smallest interior angle is the shortest side and vice versa.

Similarly, the difference between the lengths of any two sides of a triangle is always less than the length of the third side.

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

An exterior angle of a triangle is equal to the sum of its two interior opposite angles.

The sum of all exterior angles of any triangle is equal to 360°.

The sum of all interior angles of any triangle is equal to 180°.

Let us summarize some of the important properties of a triangle. Properties of Triangle: Summary & Key Takeaways

Area of a right-angled triangle = ½ * product of the two perpendicular sides.

Area of any triangle = ½ * base * height.

This is a scalene right-angled triangle since all three angles are different.

The sides opposite to these angles will be in the ratio – 1: √3: 2 respectively.

The angles of this triangle are in the ratio – 1: 2: 3, and.

This is a right-angled triangle, since one angle = 90°.

This is also called an isosceles right-angled triangle since two angles are equal.

The sides of this triangle will be in the ratio – 1: 1: √2 respectively.

Two angles measure 45°, and the third angle is a right angle.

Let’s also see a few special cases of a right-angled triangle 45-45-90 triangle

Each interior angle of an equilateral triangle = 60°.Since all the three sides are of the same length, all the three angles will also be equal.Let’s look into the six types of triangles in detail:Ī triangle that has all three sides of the same length is an equilateral triangle. Classification according to the length of its sides (Equilateral, Isosceles, Scalene).Classification according to internal angles (Right, Acute, Oblique).Triangles can be classified in 2 major ways: This is called the exterior angle property of a triangle. Any exterior angle of the triangle is equal to the sum of its interior opposite angles.The side opposite to the largest angle of a triangle is the largest side.The sum of the length of any two sides of a triangle is greater than the length of the third side.This is called the angle sum property of a triangle.

The sum of all internal angles of a triangle is always equal to 180 °.A triangle has three sides, three angles, and three vertices.Thus, we can say that a triangle is a polygon, which has three sides, three angles, three vertices and the sum of all three angles of any triangle equals 180°. When it has three line segments joined end to end. So, when does a closed figure has three angles? Properties of Triangle: Practice QuestionĪs the name suggests, the triangle is a polygon that has three angles.Properties of Triangle: Summary & Key Takeaways.– The term scalene triangle is derived from Late Latin ‘scalēnus’ and from the Ancient Greek word ‘σκᾰληνός’ which means unequal or uneven. In this triangle, angle E will be the greatest angle as it is opposite to the greatest side GO and angle O will be the smallest angle as it is opposite to the smallest side GE.Ī scalene triangle can be acute-angled or obtuse-angled or right-angled. The given triangle cannot be divided into two identical halves. The angle opposite to the longest side would be the greatest angle and vice versa.Īll sides of the given scalene triangle are unequal. Properties of the scalene triangle: All angles of a scalene triangle are unequal.Ī scalene triangle has no line of symmetry. (iii) Scalene triangle: if none of the three sides of a triangle are equal to each other, it is called a scalene triangle. (ii) Isosceles triangle: If two sides of a triangle are equal, then it is called an isosceles triangle. (i) Equilateral triangle: If all sides of a triangle are equal, then it is called an equilateral triangle. We can classify triangles according to the length of their sides. A triangle is a polygon made up of 3 sides and 3 angles.