CP GEOMETRY – REVIEW NOTES
Chapter 5 – Points of Concurrency
Circumcenter (perpendicular bisector)
Center of the circumscribed circle
y – y1 = m(x – x1) /
(x1, y1) midpoint; m is perpendicular
Incenter (angle bisector)
Center of the inscribed circle
Centroid (median)
From vertex to centroid is 2/3 the median
Short cut to finding the centroid is to average the vertices
(add and divide by 3)
Orthocenter (altitude)
y – y1 = m(x – x1) /
(x1, y1) vertex; m is perpendicular
Chapter 6 – Quadrilaterals
Sum of interior angles = (n-2)180
One interior angle (regular polygon) = n  2180
n
Exterior angle sum = 360

One interior angle (regular polygon) = 360 / n
(one interior angle) + (one exterior angle) = 180
QUADRILATERALS
TRAPEZOIDS
ISOSCELES TRAPEZOID
KITE
PARALLELOGRAM
RECTANGLE
SQUARE
RHOMBUS
Quadrilateral – 4 sided polygon
Trapezoid – one pair of parallel sides; same side angle supplementary
Isosceles Trapezoid – legs congruent; base angles congruent; diagonals
congruent
Kite – 2 pair of consecutive sides congruent; diagonals perpendicular; non-vertex
angles congruent; vertex angles bisected
Parallelogram – opposite sides parallel and congruent; opposite angles congruent;
consecutive angles supplementary; diagonals bisect each other; if there is 1 right
angle then there are 4 right angles
Rectangle – 4 right angles; diagonals congruent
Rhombus – 4 congruent sides; diagonals are perpendicular
Square – ALL OF THE ABOVE
AREA FORMULAS
trapezoid 
hb1  b2 
2
d1  d 2
2
parallelog ram  b  h
rec tan gle  l  w
d d
r hom bus  1 2
2
2
square  s
kite 

Chapter 7 – Proportions and Similarity
Triangles and polygons are similar if corresponding angles are congruent and
corresponding sides are proportional
Similarity ratio = perimeter ratio
(similarity ratio)2 = area ratio
Short Cuts to prove similarity: AA / SSS / SAS
Midsegment - segment that connects the midpoints of two sides of a triangle
Midsegment is parallel to the third side
Midsegment is ½ the third side
If a line is parallel to a side of a triangle and
intersects two sides of triangle, then
CB CD

BA DE

When triangles are similar, then perimeters, altitudes, medians and angle bisectors
are proportional.
Chapter 8 – Right Triangles and Trigonometry
Pythagorean Theorem – leg2 + leg2 = hypotenuse2 (RIGHT TRIANGLE)
Hypotenuse2 > leg2 + leg2
(OBTUSE TRIANGLE)
Hypotenuse2 < leg2 + leg2
(ACUTE TRIANGLE)
SHORT CUT TRIANGLES
30-60-90
45-45-90
TRIGONOMETRY
sin 
opposite
hypotenuse
cos 
adjacent
hypotenuse
tan 
opposite
adjacent
Chapter 11 – Area of Polygons and Circles and Volume


AREA FORMULAS
trapezoid 

hb1  b2 
2
d1  d 2
2
parallelog ram  b  h
rec tan gle  l  w
d d
r hom bus  1 2
2
2
square  s
kite 
Regular Polygon = (number of sides)[1/2 (polygon side)(apothem)]

Area of Circle = r2 (pi)
Volume = (area of base)(height)
Chapter 10 – Circles
Circumference = (diameter)(pi)
Diameter = 2 radius
arc o
arc  length 
d
360 o

If the diameter/radius is perpendicular to a chord, then it bisects both the chord and
the intercepted arc
A diameter/radius is perpendicular to a tangent at the point of tangency.
Two segments tangent to a circle from an exterior point are congruent.
ANGLES
CENTRAL ANGLE
A  arc(BC)

INSCRIBED ANGLE
B 
1
arcBD
2

VERTEX ON THE CIRCLE
B 
1
arcAB 
2

VERTEX INSIDE THE CIRCLE
BEA 

arcAB  arcCD
2
VERTEX OUTSIDE THE CIRCLE
exterior 

BIGarc  LITTLEarc
2
B 
BIGarcAC  LITTLEarcAC
2
C 
arcAD  arcBD
2
C 
arcAE  arcBD
2


