GRE
GEOMETRY
RULES
EMPOWER SUMMARY
EMPOWERgre™
MAXIMUM
MAXIMUM
IMPROVEMENT
IMPROVEMENT
MADE
MADE
EFFICIENT
EFFICIENT
Section
QUANT
Question Type
Category
ALL
GEOMETRY
NOTE: This packet is to be used in conjunction with the Modules in your
Empower GRE Course. This packet is NOT designed to be a complete
treatment of any subject herein.
GEOMETRY
16% of GRE Quant Questions
WHY you need to know Geometry:
1. Multiple Geometry questions will show up on the GRE
2. Geometry is based on a series of simple formulas. Knowing the formulas makes the questions easy to answer
Note: If a Problem Solving question includes a drawing, then that drawing is usually to scale and can be used for estimation purposes (unless the question states that the figure is NOT drawn to scale).
Note: If a Quantitative Comparison question includes a drawing, then you should NOT TRUST IT. Some QC drawings
are completely off; as such, they can not be used for estimation purposes. You can trust whatever numbers or descriptions you are given, but be suspicious of any picture that comes with a QC question
Lines
Questions involving straight lines will likely include one or more of the following rules:
1.
2.
3.
4.
Lines add up to 180°
When lines criss-cross, opposite angles equal one another
Parallel lines, when crossed by a third line, will have the same set of 2 angles show up 4 times
Perpendicular lines form 90° angles at their meeting point
Triangles
Triangle questions will involve major rules and sometimes minor rules. Be on the lookout for each of these specific
ideas on the GRE:
Major Rules:
1. Triangles add up to 180°
30°/60°/90°
45°/45°/90°
30°
45°
2. Area =
3. Pythagorean Theorem:
4. Common Pythagorean triples:
• 3, 4, 5
• 5, 12, 13
2x
x
60°
5. Multiples of those triples (for example:
• 9, 12, 15
• 50, 120, 130
45°
x
x
6. 30°/60°/90° Triangle
7. 45°/45°/90° Triangle
Sometimes the following concepts show up; not every one will, but if they show, then you need to be ready for them.
Minor Rules:
1. Isosceles Triangles – 2 sides and 2 corresponding angles are equal
2. Equilateral Triangles – 3 sides are equal, all angles are 60 degrees
3. Hidden Right Triangles – in squares or equilateral triangles
4. Triangle Inequality Theorem – with 2 sides, you can figure out the minimum length of the third side (greater than
the difference of the numbers) and the maximum (less than the sum of the numbers)
Section
QUANT
Question Type
Category
ALL
GEOMETRY
EMPOWERgre™
NOTE: This packet is to be used in conjunction with the Modules in your
Empower GRE Course. This packet is NOT designed to be a complete
treatment of any subject herein.
GEOMETRY
Polygons
Polygons include any shape with 4 or more sides and usually involve calculating an area or perimeter.
Area = base x height
Perimeter = sum of sides
Area =
Circles
ALL circle questions come down to the RADIUS. With the radius, you can solve almost any question. When a circle
interacts with another shape, pay careful attention to how the radius factors into that other shape.
Area =
Example:
Circumference =
Area =
Sector Shaded (90° is a quarter of the circle) =
Sector Area: A fraction of the area
Arc Length: A fraction of the circumference
6
Circumference =
Arc (90° carves a quarter of the circumference =
Multi-Shape
These shapes will always vary. Nevertheless, they are always combinations of the other GRE geometry rules, and
therefore rarely contains any unique rules. Break this shapes apart by looking for shapes you’re familiar with.
Note: Multi-Shape generally show up 1 time on Test Day, can take up to 3 minutes to solve, and tend to be worth very
little. Your best move on these questions is typically to TRIAGE, then come back and spend more time on them after
you’ve answered all of the other questions in the section.
Solids
Solid questions involve rectangular solids (boxes), cubes (a type of rectangular solid in which all dimensions are the
same) and cylinders (cans or tubes). They usually involve volume (what the solid will “hold”) and sometimes surface
area.
Volume = base x width x height
Volume =
Surface Area (Sum of the faces) =
Surface Area (top + bottom + side) =
Sum of:
2(base x width)
2(width x height)
2(base x height)
Section
QUANT
Question Type
Category
ALL
GEOMETRY
EMPOWERgre™
NOTE: This packet is to be used in conjunction with the Modules in your
Empower GRE Course. This packet is NOT designed to be a complete
treatment of any subject herein.
GEOMETRY
Graphing/ Functions
Graphing questions are based on simple graphing rules and concepts, including:
1.
2.
3.
4.
5.
Graphing co-ordinates (x, y)
Graphing lines (y = mx + b)
Slope (Rise/Run)
Calculating new lines based on partial information
Calculating where lines intersect one another
Slope =
Y-Axis
Equation of the line: y =
(0,0)
Section
QUANT
x+0
(3,2)
X-Axis
Question Type
Category
ALL
GEOMETRY
EMPOWERgre™
NOTE: This packet is to be used in conjunction with the Modules in your
Empower GRE Course. This packet is NOT designed to be a complete
treatment of any subject herein.