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3.1 Triangles
A triangle is a many sided figure which has three corners and three sides. Here is a picture of a triangle illustrated with some important concepts.
This is the triangle ABC.
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- Angle A is called the top angle.
- Angle B and angle C are called the base angles.
- The height always starts from the top angel and is at a right angle to the base.
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Equilateral Triangle
In an equilateral triangle all the side are equally long.
AB = BC = AC
All the angles are also equally big.
ΛA = ΛB = ΛC
ΛA = ΛB = ΛC = 60º |
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Isosceles
If a triangle has two equally longs sides, then it is an isosceles triangle.
AB = AC
The angles at the bottom (those which are connected to the long sides) are called base angles are equally big.
ΛB = ΛC
The upper angle is called the top angle. |
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Right angled triangle
If an angle of a triangle has a right angle then we called it a right angled triangle.
The two sides that create the right angle are called legs. The side which connects the two legs is called the hypotenuse. |
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Pythagorean Theorem
The sum of the squares of the legs is equal to the square of the hypotenuse.
leg2 + leg2 = hypotenuse2 |
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Obtuse Triangle
A triangle where one of the angles is obtuse, in other words greater than 90° and less than 180°. |
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Acute Triangle
A triangle where all the angles are acute, in other words less than 90°. |
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The Triangle’s Perimeter
The triangle’s perimeter is calculated by adding its three sides.
O = a + b + c |
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The Area of a Triangle
A triangle can be thought of as half of a parallelogram. If the triangle is a right-angled one, then it is half of a rectangle, like the one to the right.
The area of a rectangle is calculated by multiplying the base times the height, and then to get the triangle’s area we divide by 2.
(3.5 · 4.5) ÷ 2 ≈ 7.9 cm2
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