geometry semester 2 notes

Topics: Triangle, Pythagorean theorem, Angle Pages: 8 (1828 words) Published: October 10, 2013
Geometry Notes Second Semester
I.Area, Surface Area and Volume & Circumference
Circumference is the linear distance around the outside of a circular object. •C = π • d or π • 2r.
d = diamater or (radius • 2)
r = radius
Perimeter is the distance around a figure.
* It is found by adding the lengths of all the sides.
* Finding perimeter on the coordinate plane may require the use of the distance formula: (2 x width) + (2 x height) III.Regular Polygon
A regular polygon is a polygon that is equiangular and equilateral. • A = ½ ap
a = Apothem is distance from the center of a polygon to one of its sides. • p = ns
n = number of sides
s = length of each side
IV.Area of a Regular Polygon
Area = ½ (p • a)
p = perimeter
a = apothem
Area of a square = a*a
a = length of side
Area of a triangle= ½ b*h
b = base
h = vertical height
Area of a parallelogram = b *h
b = base
h = vertical height
Area of a trapezoid = ½ (a + b) • h
a = 1st base
b = 2nd base
h = vertical height
Area of a rectangle = b • h
b = base
h = height
X. Circle
Area of a circle = πr • r
r = radius
radius = diameter / 2
XI. Prism
A prism is a polyhedron with two congruent, parallel faces, called bases. The other faces are lateral faces. An altitude of a prism is a perpendicular segment that joins the planes of the basses. The height of a prism is the length of an altitude. In a right prism, the lateral faces are rectangles and a lateral edge is an altitude. In an oblique prism, some or all of the lateral faces are nonrectangular. XII. Lateral Area

Lateral area of a prism is the sum of the areas of all the lateral faces. •L.A. = ph
p = perimeter of the base
h = height of the prism
XIII. Surface Area
Surface area of a prism is the sum of the lateral area and the area of the two bases. •S.A. = L.A. + 2B
B = area of the base
XIV. Surface Area Pyramid
Surface Area = L.A. + B
B = base area
Lateral Area = ½ pl
p = perimeter of base
l = slant height
XV. Cones
A cone is a 3D figure with one circular base and one vertex. •Surface Area = L.A. + B
B = base area
Lateral Area = π • r • l
r = radius
l = slant height
XVI. Sphere
Surface area = 4π (r • r)
r = radius
XVII. Volume
Volume = A • L
A = area of base
L = length of prism
Volume = π (r • r) h
r = radius of base circle
h = height of cylinder
Volume = 1/3 (Ah)
A = area of base
h = height
Square Pyramids
Volume = 1/3 (l • l) h
l = length of side of base
h = height
Volume = 1/3 π (r • r) h
r = radius*
h = height
Volume = 4/3 π (r • r • r)
r = radius
XVIII. Triangles
Types of Triangles
45 - 45 - 90 Triangle
The height and base of a 45 - 45 - 90 Triangle are equal. The hypotenuse is the height or base multiplied by radical 2. 30 - 60 - 90 Triangle
The side across from the 30 degree angle is x. The hypotenuse is 2x. The side across from the 60 degree angle is x multiplied by radical 3. Isosceles Triangles
An Isosceles ∆ is a ∆ with at least 2 congruent sides. Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite to those sides are congruent. Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite to the angles are congruent. Equilateral Triangles
An Equilateral ∆ is a ∆ in which all three sides are equal. All three internal angles are also congruent to each other and are each 60°. Scalene Triangles
A Scalene ∆ is a ∆ in which all sides are not equal.
Congruency Postulates & Theorems
If three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent. •SAS Postulate
If two...
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