Adv. Geom: Final Exam
Review Topics
CHAPTER SEVEN
□ Exterior angle sum = 360 degrees
□ Ext. Angle = sum of remote int. <’s
□ Midline Theorem – half length of
base segment, parallel to base
□ No Choice Theorem
□ Triangle Congruence – SSS, SAS,
ASA, AAS, HL rt. <
□ Polygon angle sum: (n – 2)180
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Diagonal sum:
n(n  3)
2
CHAPTER EIGHT
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rise y 2  y1
Slope  m 
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run x2  x1
Horizontal line: 0 slope (ex: y = 4)
Vertical line: undef. slope (ex: x = 1)
In a proportion, the product of the
means = the product of the extremes
Geometric mean
Proving Similarity: AA, SSS, SAS
Corr. parts of similar triangles are
proportional
Side-Splitter Theorem (8.5, pg. 351)
If 3 or more parallel lines are
intersected by two transversals, the
transversals are divided
proportionally. (8.5, pg. 351)
Angle Bisector Theorem (pg. 352)
CHAPTER NINE
□ Solving quadratics
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Simplifying radicals
Rationalizing denominators
Arc measure and length
Sector area
Circle area/circumference
Altitude-on-hypotenuse Theorems
(pg. 378)
Pythagorean Theorem
Distance Formula:
d  ( y2  y1 ) 2  ( x2  x1 ) 2
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Pythagorean Triples: 3,4,5
5,12,13; 7,24,25; 8,15,17
45-45-90 Triangles
30-60-90 Triangles
Trigonometry: sine, cosine, tangent
rules (SOH CAH TOA)
Inverse trig rules: Solve for angle
measures
Angle of elevation/depression
CHAPTER TEN
Chords equidistant from the center
of a circle  Congruent chords
If chords/arcs/central angles of a
circle are congruent, then their
corresponding chords/arcs/central
angles are congruent
Radius of a circle perpendicular to a
chord  bisects the chord
Find angle and arc measures based on
vertex location (center of circle,
inscribed angles, chord-chord angles,
secant-secant angles, etc.)
A radius of a circle is perpendicular
to the point of tangency
Definition of secant
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Walk-around problems (pg. 463)
Power Theorems (10.8, pg. 493)
If an angle is inscribed in a semicircle, it is a right angle.
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C  2 r , A   r 2
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Arc length, sector area
CHAPTER ELEVEN
□ Area formulas:
 Rect/Prllgm: A = bh
 Tri: A = ½ bh
 Kite/Rhombus: A 
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1
2
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d1 d 2
Trap: A  h(b1  b2 )
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Regular Polygon:
1
2
A  12 aP
Annulus: Ring shape created by two
concentric circles
Opposite angles of inscribed quads.
are congruent
Incenter: Center of inscribed circle.
Circumcenter: Center of
circumscribed circle
Side/Area/Vol ratios (squared,
cubed, etc.)
CHAPTER TWELVE
□ Surface Area Formulas:
o Cyl LA: 2 rh
 rl
2
o Sphere: 4 r
o
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Cone LA:
Volume Formulas:
o Prism: Bh
 r 2h
o
Cylinder:
o
Pyramid: 1/3 Bh
o
Cone:
o
Sphere:
1 / 3 r 2 h
4 / 3 r 3