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1. Triangle
A triangle is a three sided polygon. A triangle has three sides, three vertices and three interior angles. The sum of the interior angles is 180°.
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Diagram 1
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The above is a triangle with vertices A, B and C and sides a, b and c, written as ΔABC.
2. Properties of triangle
- A triangle has three sides, three angles, and three vertices.
- The sum of all internal angles of a triangle equals 180°.
- The sum of the length of any two sides of a triangle is greater than the length of the third side. In the above,
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a + b > c
a + c > b
b + c > a
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- The side opposite the largest angle of a triangle is the longest side. In the above ∠A is larger than ∠B and ∠C. Notice that length a is the longest, a > b and a > c.
- Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.
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Source: storyofmathematics.com/exterior-angle-theorem
Diagram 2
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In Diagram 2 above,
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d = a + b
e = a + c
f = b + c
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3. Types of triangles
Types of triangles based on angles
The three types of triangles based on angles are:
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Type
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Property
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Acute angle triangle
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All three angles are less than 90°
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Right angle triangle
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One of the three angles equals 90°
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Obtuse angle triangle
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One of the three angles is more than 90°
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Types of triangles based on sides
The three types of triangles based on the lenghts of the sides are:
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Type
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Property
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Scalene triangle
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The three sides are not of equal length
(also, the three angles are not equal)
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Isosceles triangle
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Two of the three sides have equal length
(also, two angles are equal)
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Equilateral triangle
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All three sides have equal length
(also, all three angles are equal)
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Combining angles and sides
The names of the triangles can be combined. For instance, a right isoceles triangles is a triangle that has two sides of equal length and a 90° angle.
Example
One of the angles of a right triangle is 54°. What are the three angles of this triangle.
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180°-54°=126°
126°-90°=36° |
The three angles are 54°, 90° and 36°.
Example
Two of the angles of a triangle are 30° and 50°. What type of triangle is this?
An obtuse triangle because one of the angle is more than 90°.
Example
The lengths of the three sides of a triangle are 9 cm, 10 cm and 13 cm. Is this a scalene triangle, an isosceles triangle or an equilateral triangle?
It is a scalene triangle because the three sides are of different lengths.
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