Flashcard library · Math
Geometry: Key Theorems & Formulas
Master the essential theorems and formulas of Geometry with this focused flashcard deck. Covering everything from basic shapes like triangles and circles to polygons and 3D solids, these cards are designed to reinforce key concepts for your exams. Use them to quickly recall definitions, properties, and calculation methods vital for success in Geometry.
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What is the sum of the interior angles of any triangle?
The sum of the interior angles of any triangle is always 180 degrees.
State the Pythagorean Theorem and when it applies.
In a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): a^2 + b^2 = c^2.
What is the formula for the area of a triangle?
The area of a triangle is given by A = (1/2) * base * height, where base is one side and height is the perpendicular distance to that side from the opposite vertex.
What is the formula for the area of a rectangle?
The area of a rectangle is given by A = length * width.
What is the formula for the area of a parallelogram?
The area of a parallelogram is given by A = base * height, where base is one side and height is the perpendicular distance between the base and its opposite side.
What is the formula for the area of a trapezoid?
The area of a trapezoid is given by A = (1/2) * (base1 + base2) * height, where base1 and base2 are the lengths of the parallel sides, and height is the perpendicular distance between them.
What is the formula for the circumference of a circle?
The circumference of a circle is given by C = 2 * pi * radius (r) or C = pi * diameter (d).
What is the formula for the area of a circle?
The area of a circle is given by A = pi * radius^2 (r^2).
What is the formula for the volume of a rectangular prism?
The volume of a rectangular prism is given by V = length * width * height.
What is the formula for the volume of a cylinder?
The volume of a cylinder is given by V = pi * radius^2 (r^2) * height.
What is the formula for the volume of a sphere?
The volume of a sphere is given by V = (4/3) * pi * radius^3 (r^3).
What is the formula for the sum of the interior angles of an n-sided polygon?
The sum of the interior angles is given by (n - 2) * 180 degrees, where n is the number of sides.
When two parallel lines are cut by a transversal, what is the relationship between alternate interior angles?
Alternate interior angles are congruent (equal in measure).
State the Triangle Inequality Theorem.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
What is the formula to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane?
The distance d is given by d = sqrt((x2 - x1)^2 + (y2 - y1)^2).