1. Interesting Geometry Facts and Tactics

2. Lines and Angles
Angles are classifies according to their degree measures
Acute: less than 90 degrees.
Right angle = 90 degrees.
Obtuse: more than 90 degrees, but less than 180 degrees.
A straight angle measures 180 degrees
Vertical angles have equal measures

3. Circles Diameter is the longest chord than can be drawn in a circle
If d is the diameter and r is the radius of a circle, d=2r
Formulas
π= circumference/diameter = C/d
C= πd or C= 2 πr
A= πr2
The degree measure of a complete circle is 360 degrees

4. Circles Continued
Any triangle formed by connecting the endpoints of two radii is isosceles.
The degree measure of an arc equals the degree measure of the central angle that intercepts it
If an arc measures x degrees, the length of the arc is x / 360 (2πr), and the area of the sector formed by the arc and 2 radii is x / 360 (πr2)
If a line is tangent to a circle, a radius (or diameter) drawn to the point where the tangent touches the circle is perpendicular to the tangent line.

5. Quadrilaterals and Other Polygons
In any quadrilateral the sum of the measures of the four angles is 360°
The sum of the measures of the n angles in a polygon with n sides is (n-2) * 180°
In a regular polygon the measure of each interior angle is [(n-2)(180)] / n and the measure of each exterior angle is 360 degrees / n
In any polygon, the sum of the exterior angles taking one at each vertex, is 360°

6. Parallelograms Parallelograms have the following properties:
Opposite sides are equal: AB=CD and AD=BC
Opposite angles are equal: a=c and b=d
Consecutive angles add up to 180°
The two diagonals bisect each other: AE=EC and BE=ED
A diagonal divides the parallelogram into two triangles that have the exact same size and shape (the triangles are congruent)

7. Formulas You Should Know
Area of a parallelogram: A=bh
Area of a rectangle: A=LW
Area of a square: A=
Area of a trapezoid: A=
Rectangular Solid: V = lwh, A= 2(lw + lh + wh)
Cube: V = eee = e3, A = 6e3
Cylinder: V = 2r2h, A =2rh

8. Coordinate Geometry
The distance, d, between two points, A (x1, y1) and B (x2, y2), can be calculated using the distance formula: d = √(x2 – x1)2 + (y2 – y1)2
Vertical lines do not have slopes
To find the slope of any other line proceed as follows:
Choose any two points A(x1, y1) and B (x2, y2) on the line.
Take the differences of the y-coordinates, y2 – y1, and the x-coordinates, x2 – x1 .
Divide: slope = (y2-y1) / (x2-x1)

9. Tactics for Geometry Problems
Draw a Diagram (if one is not given)
Never ASSUME a diagram has been drawn to scale
Exaggerate or change a diagram when needed
Add a Line to a diagram
Subtract to Find Shaded Regions

10. Draw a diagram
For questions that are related to geometry, draw a figure that represents the problem
Do not attempt the problem without drawing a diagram

11. Never ASSUME a Diagram Has Been Drawn to Scale
Only trust diagrams that are drawn to scale. If the diagrams are drawn to scale, you may use an observation to accurately estimate the sizes of the angles and line segments
If a diagram is given and appears to be drawn to scale, trust it.
If a diagram is given but has not been drawn to scale, try to draw it to scale on your scrap paper, and then trust it
When no diagram is provided, and you draw one on your scrap paper, try to draw it to scale.

12. Exaggerate or Otherwise Change a Diagram
Sometimes it is appropriate to take a diagram that appears to be drawn to scale and intentionally exaggerate it.
This tactic is especially beneficial for Quantitative Comparison Questions

13. Add a Line to a Diagram
Occasionally, after staring at a diagram, you still have no idea how to solve the problem to which it appears.
It looks as though not enough information has been given.
When that happens, it often helps to draw another line in the diagram

14. Subtract to Find Shaded Regions
Whenever part of a figure is shaded, the straightforward way to find the area of the shaded portion is to find the area of the entire figure and subtract the area of the non-shaded region
If asked to find the area of the non-shaded region, you can subtract the shaded area from the total area
Occasionally, you may see an easy way to calculate the shaded area directly, but usually you should subtract