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GEOMETRY FINAL REVIEW
Similar Triangles
PROPORTIONS To solve a proportions
Cross multiplySolve
EXAMPLE
SIMILAR FIGURES1. Write the proportions for
corresponding sides
2. Solve the proportion
EXAMPLE
EXAMPLE
EXAMPLE
GEOMETRIC MEANThe geometric mean of two numbers is the square root of the product of the numbers.
a b
EXAMPLEFind the geometric mean of the two numbers. Simplify your answer.1. 7 and 35
GEOMETRY FINAL REVIEW
Right Triangles
PYTHAGOREAN THEOREMa2 + b2 = c2
ca
b
EXAMPLE
TRIGONOMETRIC RATIOSSin A =
Cos A =
Tan A =
hypotenuse
opposite
hypotenuse
adjacent
adjacent
opposite
EXAMPLEFind the value of sine, cosine, and tangent ratios to the nearest hundredth.
SOLVING TRIANGLES FOR ALL MISSING PARTSIf you know two sides and one angle: To find the missing side use Pythagorean
theorem:a2 + b2 = c2
To find the two angles use inverse trigonometric functions:
Angle = Sin -1
Angle = Cos -1
Angle = Tan -1
hypotenuse
opposite
hypotenuse
adjacent
adjacent
opposite
If you know two angles and one side: To find the missing angle:
Add the two angles and subtract from 1800
To find the two missing sides use the trigonometric ratios.
Sin angle =
Cos angle =
Tan angle =
hypotenuse
opposite
hypotenuse
adjacent
adjacent
opposite
EXAMPLESolve each triangle for all the missing information. Round your answer to the nearest tenth.
EXAMPLESolve each triangle for all the missing information. Round your answer to the nearest tenth.
GEOMETRY FINAL REVIEW
Circles
ARCS & ANGLES Central Angle
Angle = Arc
Inscribed AngleAngle = ½ Arc
Inside the circleAngle = ½ (sum of the arcs)
Outside the circleAngle = ½ (difference of the arcs)
EXAMPLEFind the measure of the missing angle or
arc.
EXAMPLEFind the measure of the missing angle or
arc.
EXAMPLEFind the measure of the missing angle or
arc.
CHORDS & SECANTS Inside the circle
Part ∙ Part = Part ∙ Part
Outside the circle Outside ∙ Whole = Outside ∙
Whole
E
C
AB
D
B
EC
D
A
A
EC
D
EXAMPLESolve for x.
EXAMPLESolve for x.
ARC LENGTH/CIRCUMFERENCE C = 2pr
B
A
03602
mAB
r
ABoflengthArc
EXAMPLE:Find the length of arc BC. Leave your answer in terms of .p
7 in
40o
SECTOR AREA/AREA A = p r2
P
D
C
02 360
mAB
r
A
EXAMPLE:Find the area of the shaded region. Leave your answer in terms of .p
7 in300
GEOMETRY FINAL REVIEW
Area of Polygons
AREA/PERIMETERY OF POLYGONS Circle
C = 2 p rA = p r2
SquaresP = 4sA = s2
RectanglesP = 2L + 2WA = L W
r
s
L
W
AREA/PERIMETERY OF POLYGONS Parallelograms
P = 2b + 2lA = b h
TrapezoidsP = add up all 4 sidesA = ½ (b1 + b2) h
TrianglesP = a + b + cA = ½ b h
b
lh
b2
b1
h
a
c
b
AREA OF EQUILATERAL TRIANGLES
P = 3sA = ¼ s2 √3
s
AREA OF REGULAR POLYGONS Given side length and apothem
P = n sA = n [ ½ (s)(a)]
a s
AREA OF REGULAR POLYGONS Given side length only
P = n s To find a
1. = 360/2b n2. x = s/23. a = x/tan b4. A = n [ ½ (s)(a)] sb
EXAMPLE:Find the perimeter and area of each
polygon.1.
2.
Find the area of the regular polygons.1.
2 ft
GEOMETRY FINAL REVIEW
Surface Area & Volume
IMPORTANT TERMS FOR SURFACE AREA & VOLUME B = Area of the Base
Base is the shape not like the others Base does not mean the bottom shape Base is not one number it is an area (use the
previous chapter)
P = Perimeter of the Base
h = height of the polyhedron
l = slant height of the polyhedron
SURFACE AREA & VOLUME FORMULAS Prism
SA = 2B + Ph
V = Bh
PyramidSA = B + ½ P l
V = 1/3 B hB
h l
SURFACE AREA & VOLUME FORMULAS Cylinder
SA = 2 p r2 + 2 p r h
V = p r2 h
ConeSA = p r2 + p r l
V = 1/3 p r2 h r
h l
h
r
SURFACE AREA & VOLUME FORMULAS Sphere
SA = 4 p r2
V = 4/3 p r3
r
GEOMETRY WARM-UPAPRIL 29, 2014Find the surface area and volume of the right prism.1.
5 in9 in
2 in
GEOMETRY WARM-UPAPRIL 29, 2014Find the surface area and volume of the right pyramid.1.
7 in7 in
9 in
