Chapter 11/12 Theorems/Postulates/ Collaries
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| Area of a Square postulate | the area of a square is the square of the length of its side, or A=s squared
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| Area Congruence postulate | if two polyhedrons are congruent, then they have the same area
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| Area Addition postulate | the area of a region is the sum of the areas of all its overlapping parts
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| Volume of a Cube | the volume of a cube is the cube of the length of its side, or V=s cubed
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| Volume Congruence postulate | If two polyhedra are congruent, then they have the same volume
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| Volume Addition postulate | the volume of a solid is the sum of the volumes of all its overlapping parts
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| Area of Rectangle | the area of a rectangle is the product of its base and height; A=bh
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| Area of a Parallelogram | the area of a parallelogram is the product of a base and its corresponding height; A=bh
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| Area of a Triangle | the area of a triangle is one half the product of the base and its corresponding height; A=1/2bh
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| Area of a Trapezoid | the area of a trapezoid is one half the product of the height and the sum of the lengths of the + bases; A=1/2h[b(1)+b(2)]
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| Area of a Rhombus | the area of a rhombus is one half the product of the lengths of its diagonals; A=1/2d(1)x d(2)
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| Area of a Kite | the area of a kite is one half the product of the lengths of its diagonals; A=1/2d(1)x d(2)
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| Area of Similar Polygons | if two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a squared: b squared
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| Circumference of a Circle | the circumference C of a circle is C = pie x d or C = 2 x pie x r, where d is the diameter of the circle and r is the radius of the circle
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| Arc Length Corollary | in a circle, the ratio of the length of a given arc to the the circumference is equal to the ratio of the ratio of the measure of the arc to 360 degrees.
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| Area of a Circle | the area of a circle is pie times the square of the radius; A = pie x r squared
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| Area of a Sector | the ratio of area A of a sector of a circle to the area of the whole sector of a circle to the area of the whole circle (pie x r squared) is equal to the ratio of the measure of the intercepted arc to 360 degrees; A/pie x r squared = m arc AB/360 degrees,
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| Area of a Regular Polygon | the area of a regular n-gon with side length s is half the product of the apothem a and the perimeter; P, so A = 1/2aP, or A=1/2a x ns
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| Euler's Theorem | the number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2
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| Surface Area of a Right Prism | the surface area S of a right prism is S = 2B + Ph = aP + Ph, where is the apothem of the base, B is the area of a base, P is the perimeter of a base, and h is the height
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| Surface Area of a Right Cylinder | the surface area S of a right cylinder is S = 2B + Ch = 2 x pie x r squares + 2 x pie x r x h, where B is the area of a base, C is the circumference of a base, r is the radius of a base, and h is the height
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| Surface Area of a Regular Pyramid | the surface area S of a regular pyramid is S = B + 1/2Pl, where B is the area of the base, P is the perimeter of the base, and l is the slant height
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| Surface Area of a Right Cone | the surface are S of a right cone is S = B + 1/2Cl = pie x r squared + pie x r x l, where B is the area of a the base, C is the circumference of the base, r is the radius of the base, and l is the slant height
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| Volume of Prism | the volume V of a prism is V = Bh, where b is the area of a base and h is the height
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| Volume of a Cylinder | the volume V of a cylinder is V=Bh=pie x r squared x h, where B is the area of a base, h is the height, and r is the radius of a base
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| Cavalieri's Principle | if two solids have the same height and the same cross-sectional area at every level, then they have the same volume
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| Volume of a Pyramid | the volume V of a pyramid is V = 1/3Bh = 1/3 x pie x r squared x h, where b is the area of the base, h is the height, and r is the radius of the base
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| Surface Area of a Sphere | the surface area S of a sphere with radius r is S=4 x pie x r cubed
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| Volume of a Sphere | the volume V of a sphere with radius r is V = 4/3 x pie x r
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| Similar Solids Theorem | if two similar solids of a:b, then corresponding areas have a ratio of a squared:b squared, and corresponding volumes have a ratio of a cubed:b cubed
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