Triangle
Three sides connected to each other resulting a closed contour is known as triangle. As shown in the figure below, it’s edges and angles are represented in this format: Angles are represented with capital letter A, B and C (or sometimes written as ∠BAC, ∠ABC and ∠ACB) and the edge opposite to angles A, B and C are named as a, b and c respectively.
Properties:
- It has three angles each at the joining of two sides
- All three angles of a triangle sum to 180
- The ratio of side length to the sine of its opposite angle is the same for all three sides. Mathematically, it can be expressed as
- \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
- Perimeter of triangle, 2s = a + b + c
- Area of triangle if height is given = \frac{1}{2} \times \text{base}(a) \times \text{height}(h)
- Area of triangle = \sqrt{s(s-a)(s-b)(s-c)} Where s is the half of its perimeter
Parallelogram:
A parallelogram is a four sided shape which is described by following properties:
Properties:
- Opposite sides are parallel to each other
- Opposite sides are equal in length
- Diagonals of parallelogram bisects each other
- Sum of all interior angles are equal to 360o
- None of the angles equal to 90o
- Opposite angles are equal
- Perimeter = 2(AB+AD)
- Area = \text{base} \times \text{height} = AB\times h
Rhombus
A rhombus is a four sided shape which is described by following properties
Properties:
- Opposite sides are parallel to each other
- All sides are equal in length
- Diagonals of rhombus are perpendicular bisector
- Sum of all interior angles are equal to 360o
- None of the angles equal to 90o
- Opposite angles are equal
- Perimeter = 4a (where a is the length of a side)
- Area = \frac{1}{2} \times \text{diagonal element1} \times \text{diagonal element2}
Rectangle
A rectangle is a four sided shape with the following properties
Properties:
- Opposite sides are parallel to each other
- Opposite sides are equal in length
- Diagonals of rectangles are equal and bisects each other
- Sum of all interior angle are equal to 360o
- Each of the interior angle is equal to 90o
- Perimeter = 2×(AB+AD)
- Area = AB×AD
Square
A square is a four sided shape with the following properties
- Opposite sides are parallel to each other
- Diagonals of squares are equal
- Diagonals of squares are perpendicular bisector
- All sides are equal in length
- Sum of all interior angle are equal to 360o
- Each of the interior angle is equal to 90o
- Perimeter = 4×AB
- Area = AB2
Circle
A circle is defined by its center, c and radius, r such that distance of any point on circle from its center is always equal to its radius. Circle has the following properties
- Diameter is defined as the line drawn from any point on circle, passes through the center, ends at other point on circle. Diameter, d = AB = 2r
- Perimeter = 2πr
- Area = πr2
- Any triangle drawn on semicircle is always a right triangle. Triangle ACB is right triangle.
- Any segment of circle is known as arc
- Angle created by an arc at the center is twice as the angle created by the same arc on the circumference. \angle DOF = 2 \angle DEF
Trapezoid
A trapezoid is a four sided shape with only one pair of sides are parallel. It has the following properties:
- Two sides are parallel and other two sides are nonparallel
- Opposite angles are supplementary and sum of opposite side angles are 180o
- Perimeter = AB + BC + CD + AD
- Area = \frac{1}{2} \times \text{sum of parallel sides} \times \text{height} = \frac{1}{2}(a+b)h
Polygon
A polygon is a general term which is defined by the number of sides it encompasses. For example, a three side polygon is known as triangle, a five side polygon is known as pentagon.
Properties
- Number of diagonals of a polygon = \frac{n(n-3)}{2} where n is the number of vertices in the polygon
- Sum of interior angles of polygon = (n-2)\times 180^\circ where n is the number of sides.