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Here I am going to post a GMAT Geometry Cheat Sheet which can be used to review most of the concepts and Formula for Geometry
ESSENTIAL PROPERTIES OF TRIANGLES
Area = ½ (Base)(Height)
Isosceles Triangles: Two sides identical; Two angles identical
Equilateral Triangles: All three sides equal in length. All three angles 60 degrees.
Right Triangles: One angle 90 degrees, opposite the longest side (hypotenuse).
Pythagorean Theorem: a2 + b2 = c2 (with c as the hypotenuse of a right triangle)
ESSENTIAL PROPERTIES OF CIRCLES
Radius = distance from the midpoint to the circle
Diameter = distance across the circle through the midpoint
Area = πr2
Circumference = 2πr or πd
Arc Length = Circumference • (central angle)/360
Chord = Line that connects any two points on a circle
Tangent = A line that touches a circle at only one point. At the point of tangency, the tangent is perpendicular to the diameter
Diameter of a circle = hypotenuse of a right triangle with any point on the outside
ESSENTIAL PROPERTIES OF COORDINATE GEOMETRY
The x-axis is horizontal and the y-axis is vertical
Points are plotted in the order (x, y)
To calculate the distance between two points, use the Pythagorean Theorem.
Lines are plotted using the equation y = mx + b
m = the slope of the line
b = the y-intercept (where the line crosses the y-axis)
-b/m = the x-intercept (where the line crosses the x-axis)
The slope of a line: (“rise over run”)
The midpoint between two points: (the average of the two x coordinates and the average of the two y coordinates)
ESSENTIAL PROPERTIES OF 3-DIMENSIONAL FIGURES
Cube: A square with a depth component.
Volume = (side)3
Surface area = 6(side)2
Cylinder: A circle with a height component.
Volume = area of a circle • height of the cylinder
Surface area = area of two circles + area of the rectangle formed by the height of the cylinder and the circumference of the circle.
Rectangular box: A rectangle with a height component.
Volume = length • width • height
Surface area = Add the areas of all six sides.
ESSENTIAL PROPERTIES OF TRIANGLES
Area = ½ (Base)(Height)
Isosceles Triangles: Two sides identical; Two angles identical
Equilateral Triangles: All three sides equal in length. All three angles 60 degrees.
Right Triangles: One angle 90 degrees, opposite the longest side (hypotenuse).
Pythagorean Theorem: a2 + b2 = c2 (with c as the hypotenuse of a right triangle)
ESSENTIAL PROPERTIES OF CIRCLES
Radius = distance from the midpoint to the circle
Diameter = distance across the circle through the midpoint
Area = πr2
Circumference = 2πr or πd
Arc Length = Circumference • (central angle)/360
Chord = Line that connects any two points on a circle
Tangent = A line that touches a circle at only one point. At the point of tangency, the tangent is perpendicular to the diameter
Diameter of a circle = hypotenuse of a right triangle with any point on the outside
ESSENTIAL PROPERTIES OF COORDINATE GEOMETRY
The x-axis is horizontal and the y-axis is vertical
Points are plotted in the order (x, y)
To calculate the distance between two points, use the Pythagorean Theorem.
Lines are plotted using the equation y = mx + b
m = the slope of the line
b = the y-intercept (where the line crosses the y-axis)
-b/m = the x-intercept (where the line crosses the x-axis)
The slope of a line: (“rise over run”)
The midpoint between two points: (the average of the two x coordinates and the average of the two y coordinates)
ESSENTIAL PROPERTIES OF 3-DIMENSIONAL FIGURES
Cube: A square with a depth component.
Volume = (side)3
Surface area = 6(side)2
Cylinder: A circle with a height component.
Volume = area of a circle • height of the cylinder
Surface area = area of two circles + area of the rectangle formed by the height of the cylinder and the circumference of the circle.
Rectangular box: A rectangle with a height component.
Volume = length • width • height
Surface area = Add the areas of all six sides.
12 Aug 2023, 10:23
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