Geometry EOC FSA Mathematics Reference Sheet

The Geometry EndofCourse (EOC) Florida Standards Assessment (FSA) tests students on the key concepts, skills, and reasoning abilities outlined in the Florida Mathematics Sunshine State Standards for Geometry. This reference sheet consolidates the most essential formulas, definitions, and strategies students need to succeed on the exam. Use it as a quicklook guide while studying or as a review tool before test day.

1. Foundations of Geometry

1.1. Basic Definitions

• Point Location with no size.
• Line Infinite set of points extending in opposite directions.
• Line Segment Part of a line bounded by two endpoints.
• Ray Part of a line with a single endpoint extending infinitely in one direction.
• Plane Flat surface extending infinitely in all directions.
• Angle Region formed by two rays sharing a common endpoint (vertex).

1.2. Types of Angles

2. Transformations

2.1. Rigid Motions

• Translation Slides a figure without rotating or flipping it.
• Rotation Turns a figure around a fixed point (center) by a given angle.
• Reflection Flips a figure across a line (line of symmetry).

2.2. Dilations

A dilation changes size but not shape. If the scale factor is k:

• Lengths koriginal length
• Area koriginal area
• Perimeter koriginal perimeter

3. Congruence & Similarity

3.1. Triangle Congruence Criteria

• SSS Three sides equal.
• SAS Two sides and the included angle equal.
• ASA Two angles and the included side equal.
• AAS Two angles and a nonincluded side equal.
• HL (Righttriangle) Hypotenuse and one leg equal.

3.2. Triangle Similarity Criteria

• AA Two angles equal.
• SSS Corresponding sides in proportion.
• SAS Two sides in proportion with included angle equal.

4. Quadrilaterals & Polygons

4.1. Common Quadrilaterals

4.2. Area Formulas

• Rectangle: A=lw
• Square: A=s
• Parallelogram: A=bh
• Triangle: A=bh
• Trapezoid: A=(b+b)h
• Rhombus: A=dd (product of diagonals) or A=bh
• Circle (for related problems): C=2r, A=r

5. Coordinate Geometry

5.1. Distance Formula

For points (x,y) and (x,y):

d=[(xx)+(yy)]

5.2. Midpoint Formula

Midpoint M of segment AB:

M=( (x+x)/2 , (y+y)/2 )

5.3. Slope

Slope of line through (x,y) and (x,y):

m=(yy)/(xx)

Perpendicular lines: product of slopes =1.

6. Circles

6.1. Key Terms

• Radius (r) Distance from center to any point on the circle.
• Diameter (d) Twice the radius; passes through the center.
• Circumference (C) Length around the circle: C=d=2r.
• Chord Segment connecting two points on a circle.
• Arc Part of the circumference between two points.
• Sector Region bounded by two radii and the included arc.

6.2. Area of Sector

For central angle (in degrees):

Area=(/360)r

7. Proof Strategies

• Write a clear statement: Identify what is given and what must be proven.
• Use known theorems: Vertical angles, corresponding angles, properties of parallel lines, triangle sum (180), angleaddition, and supplementary angles.
• Show work in a logical sequence: Each step should follow from the previous one, citing the theorem used.
• Diagram matters: Draw accurate, labeled figures; use color or shading to highlight relationships.
• Check the converse: Sometimes proving the converse of a theorem is required (e.g., if corresponding angles are congruent, lines are parallel).

8. Common Problem Types

8.1. Finding Missing Lengths

Apply appropriate formulas (Pythagorean theorem for right triangles, similarity ratios, or properties of special quadrilaterals).

8.2. Angle Measures

Use linear pair, vertical, and supplementary relationships, as well as parallel line angle theorems.

8.3. Area & Perimeter

Break complex figures into known shapes, use additive properties, and remember to include all sides.

8.4. Coordinate Problems

Calculate distances, slopes, and midpoints; verify collinearity or perpendicularity using slope relationships.

8.5. Proof Writing

Combine algebraic statements with geometric reasoning; justify every claim.

9. TestTaking Tips

• Read each question twice. Identify key words such as congruent, similar, parallel, or distance.
• Eliminate clearly wrong answer choices. This increases the odds when you must guess.
• Sketch quickly. A rough diagram can reveal relationships that are otherwise hidden.
• Watch for common traps. For example, confusing a diameter for a chord, or assuming a quadrilateral is a rectangle without justification.
• Time management. Allocate roughly 12 minutes per multiplechoice item; flag difficult problems for a second review.
• Use the calculator wisely. Its allowed for the EOC; avoid rounding until the final answer.

10. Quick Reference Tables

10.1. Triangle Area Formulas

10.2. Circle Segment & Sector Relationships