The area of a geometric shape is a property that describes how much space it takes up.
Perimeter is the outermost parts or boundary of an area or object.
Surface Area is the total area of the surface of a three-dimensional object.
A diagonal is a line segment linking to non-adjacent vertices in a polygon or polyhedron. Any sloping line is called diagonal.
A vertex is a point where two or more line segments meet.
An angle is the figure formed by two rays, sharing a common endpoint.
A ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.
Point is a location in space or a dot on a piece of paper
A line connects two points via the shortest path and continues indefinitely in both directions.
Line segment is a part of a line between two points
Perpendicular line segment is a line segment that intersect or cross at an angle of 90 degrees.
Parallel Line Segments are line segments that never intersect and they are always the same distance apart.
Radius is the distance from center of a circle to any point on the circle's circumference
Circumference is the distance around a circle or perimeter
Diameter is a line segement joining two points on a circles circumference and passes through the circle's center or twice the length of the radius.
Radian: the angle made when we take the radius and wrap it round the circle.
volume: the 3-dimensional space enclosed by a boundary or occupied by an object.
A^2 + B^2= C^2
Used to determine the Length of the hypotenuse, which is the longest side of a right triangle.
Parallelogram:
A quadrilateral with two pairs of opposite sides parallel.
Area =
Properties of Parallelogram
The degree measure of the four angles of a parallelogram add up to 360 degrees.
The degree measure of any two consecutive angles add up to 180 degrees.
Opposite angles have the same measure in terms of degrees.
Opposite sides are parallel
Opposite sides have the same lengths
The diagonals of a parallelogram divide the parallelogram into two side-by-side triangles
Diagonals of a parallelogram bisect each other
Circle:
A circle is a closed curve formed by a set of points on a plane that are the same distance from its center.
Circumference = π × Diameter or 2 × π × Radius
Diameter = 2 × Radius
Angles
An angle consists of two rays that share the same endpoint. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.
There are four types of angles: acute, right, obtuse, and straight.
Acute: is less than 90°
Right: is 90° exactly
Obtuse: is greater than 90° but less than 180°
Straight: is 180° exactly
Reflex Angle: is greater than 180°
Full Rotation is 360° exactly
Two angles with the same measure are called congruent angles
Supplementary angles: are two angles whose sum is 180 degrees
complementary angles: are two angles whose sum is 90 degrees
1 Radian is equal to 57.2958
To go from radians to degrees: multiply by 180, divide by π
To go from degrees to radians: multiply by π, divide by 180
Triangles
A triangle is a polygon that has three sides, three angles, and three vertices.
Properties of a Triangle
The sum of all three interior angles of any triangle equals to 180 degrees. This is called the angle sum property of a triangle.
The sum of all exterior angles of any triangle is equal to 360 degrees.
The sum of the length of any two sides of a triangle is greater than the length of the third side.
The side opposite to the largest angle of a triangle is the largest side.
In case of a right-angled triangle, this side is called the hypotenuse
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.
Classification of Triangles
Triangles can be classified in two different ways:
Acute: all three angles less than 90 degrees
Right: has one angle that measures exactly 90 degrees
Obtuse/Oblique: one angle that measures more than 90 degrees
Equilateral: all three sides of the triangle are the same length
Isosceles: two sides of the triangle have the same length and the third side has a different length
Scalene: all three sides of the triangle are different lengths
Rectangle:
A quadrilateral in which all the angles are right angles and has opposite sides that have equal length and are parallel.
Properties of An Rectangle
Each of the interior angles of a rectangle is 90∘.
The diagonals of a rectangle bisect each other and are equal in length.
The opposite sides of a rectangle are parallel and equal.
To calculate the Area of a rectangle you would do height times width
Area = height x width
The perimeter of a rectangle is the sum of the length of its four sides.
Perimeter = 2(length + Width)
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Geometry youtube prep videos from Math Fortress
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Youtube Video lessons on Geometry from Math Fortress
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Square
Properties of a Square
All four interior angles are equal to 90°
All four sides of the square are congruent or equal to each other
The opposite sides of the square are parallel to each other
The diagonals of the square bisect each other at 90°
The two diagonals of the square are equal to each other
The square has 4 vertices and 4 sides
The diagonal of the square divide it into two similar isosceles triangles.
Area of the square is equal to the side squared
Area = side2 per square unit
The perimeter of the square is equal to the sum of all its four sides.
Perimeter = 4 × side of the square or P = 4s
The length of the diagonals of the square is equal to s√2, where s is the side of the square.
d = s√2
Where d is the length of the diagonal of a square and s is the side of the square.
Trapezoid:
A quadrilateral with exactly one pair of opposite sides parallel.
Area = 
Perimeter = All sides added together
P= a + b + c + d.
| Cube |  |
Volume = x³ Surface area = 6x² |
| Cuboid |  |
Volume = xyz Surface area = 2xy + 2xz + 2yz |
| Cylinder |  |
Volume = π r²h Area of curved surface = 2π rh Area of each end = π r² Total surface area = 2π rh + 2π r² |
| Prism |  |
A prism has a uniform cross-section Volume = area of cross section × length = A l |
Three dimensional Figures
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Three-dimensional shapes have thickness or depth.
Cylinder: is a closed solid that has two parallel (usually circular) bases connected by a curved surface.
Cone: is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex
Cube: is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. It has 6 faces, 12 edges, and 8 vertices.
Rectangular prism: a 3-dimensional solid shape which has six faces that are rectangles.
Triangular Prism: a prism composed of two triangular bases and three rectangular sides.
Pyramid: a three-dimensional structure whose base is a polygon and its base and top forms a triangle.
Sphere: a geometrical figure that is perfectly round, 3-dimensional and circular
Calculating surface area
The surface area of a cube is the area of one face (length x width) multiplied by 6, because all six faces are the same.
Surface area of a Prism =2lw+2lh+2hw
Surface Area of a Sphere = 4πr 2
Surface Area of a Cylinder = 2(πr 2 ) + (2πr) x h
Surface area of a Pyramid can be calculated by first multiplying the perimeter of the pyramid by its slant height. Then, divide that number by 2. Finally, add the number you get to the area of the pyramid's base to find the surface area.
Lateral surface area of a regular pyramid is L.S.A.=1/2 x perimeter of base x Slant height
Total surface area of a regular pyramid is T.S.A.=1/2 x perimeter of base x Slant height + area of the base