Honors Geometry
Final Exam Study Guide
Name _____________________
Relationships in Triangles
1. Medians and altitudes
2. Centroid- point of concurrency of the medians of a triangle
3. Orthocenter - point of concurrency of the altitudes of a triangle
Polygons
1. Midsegment theorem – A segment joining the midpoints of 2 sides of a triangle is parallel to the third side
and half the length of the third side.
2. Names of polygons
3. Polygon formulas:
Sum of interior angles S I  (n  2)180
Sum of exterior angles S E  360
(n  2)180
or I  180  E
n
360
One exterior angle (Reg. Polygon) E 
or E  180  I
n
n(n  3)
Total number of diagonals d 
2
5. Quadrilaterals and their properties – parallelogram, rectangle, rhombus, square, trapezoid, isosceles
trapezoids, kite
One interior angle (Reg. Polygon) I 
6. Varignon's Theorem - If the midpoints of a figure are joined in order, the new figure formed is a
parallelogram.
Similar Polygons
1. Ratio and proportion
2. Similarity and dilations
3. The ratio of the perimeters of 2 similar polygons equals the ratio of any pair of corresponding sides.
P1 s1

P2 s 2
4. Similar triangles (AA, SAS~, SSS~)
5. Side-Splitter Theorem
x
a
a x

b y
b
y
6. Angle Bisector Theorem
c d

x y
d
c
x
y
The Pythagorean Theorem
1.
Skills with radials (simplifying, adding/subtracting, multiplying/dividing)
2.
Altitude to hypotenuse theorem
leg
alt
seg1
leg
seg2
hyp
3.
Pythagorean Theorem
Main Triples Families:
Converse of Pythagorean Theorem: If
, then triangle is acute
If
, then triangle is right
If
, then triangle is obtuse
Zig-Zag Problem
4.
Special Right Triangles
45
30
60
45
Trigonometry
Circles
1.
Vocabulary and theorems
2.
3.
Tangents and tangent circles
4.
Common-tangent procedure
5.
Walk-around problems
6.
Angles and arcs of a circle
7.
If a quadrilateral is inscribed in a circle, the opposite angles are supplementary.
8.
A parallelogram inscribed in a circle is a rectangle.
9.
An angle inscribed in a semicircle is a right angle.
10.
Special segments in a circle
Area
Area of a rectangle:
Area of a square:
Area of a parallelogram:
Area of a triangle:
[Heron’s Formula]
or
Area of an equilateral triangle:
Area of a trapezoid:
Area of a rhombus or kite:
Area of a regular polygon:
Area of a circle:
or
Area (continued)
Circumference of a circle:
or
Length of an arc of a circle:
Area of a sector of a circle:
Area of a segment of a circle: Area of sector – area of triangle
Coordinate Geometry
Midpoint:
Slope:
Horizontal lines have 0 slope.
Vertical lines have no slope.
Distance formula:
Equations of lines:
Slope-intercept form
Point-slope form