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Right angle triangle: A triangle where one of its interior angles is a right angle 90°.
Area:
Area (A) = 1/2(b × h)
Thus, the height of the triangle h = Area × 2 / b
And, the base of triangle b = Area × 2 / h
Where h is denoted as height.
Where b is denoted as base.
The perimeter:
a² + b² = c²
a, b are the lengths of the other two sides.
Where c is the length of the hypotenuse.
Sides: The two sides that are not the hypotenuse makes the right angle.
Hypotenuse: The side opposite the right angle is called the hypotenuse. It will always be the longest side of a right triangle.
Properties:
- If the two sides that include the right angle are equal in length (AB and BC), then it said to be an isosceles triangle.
- The hypotenuse (the side opposite the right angle) is always longer than either of the other two sides so it can never be an equilateral triangle.
Isosceles triangle: A triangle which has two of its sides equal in length.
Area:
Area (A) = 1/2(b × h)
Thus, the height of the triangle h = Area × 2 / b
And, the base of the triangle b = Area × 2 / h
Where h is denoted as height.
Where b is denoted as base.
Altitude h = √( a² - b²) / 4
The perimeter:
P = 2a + b
Where a is the lengths of the two equal sides.
Where b is the lengths of the other sides.
Properties:
- The 'base' of the triangle is referred to the unequal side of an isosceles triangle.
- The base angles of an isosceles triangle are always equal. (∠ABC and ∠ACB are always the same)
- The altitude is a perpendicular distance from the base to the topmost vertex.
Important!
- When the 3rd angle is a right angle, it is called a "right isosceles triangle".
- If all three sides are the same length, it is called an equilateral triangle.
- All the equilateral triangles will have all the properties of an isosceles triangle.
Equilateral triangle: A triangle which has all three of its sides equal in length.
Area:
Area (A) = √3/4 s².
Where s² denotes sides of the triangle.
The perimeter:
Perimeter (P) = a + b + c or P = s + s + s.
a, b, c are the lengths of the three equal sides.
or
s is the lengths of the three equal sides.
Properties:
- All three angles of an equilateral triangle are always 60°. Hence, ∠ABC, ∠CAB and ∠ACB are always the same. Since the angles are the same and the internal angles of any triangle always add to 180°, each is 60°.
- An equilateral triangle is one in which all three sides are congruent (same length). Because it also has the property that all three interior angles are equal.
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