Geometry

Question 1

A line is a … angle When two lines intersect, … angles are formed; the sum of these angles is… When two lines are perpendicular to each other, their intersection forms …. angles …. angles are also called ….

Answer 1

A line is a 180-degree angle. When two lines intersect, four angles are formed; the sum of these angles is 360 degrees. When two lines are perpendicular to each other, their intersection forms four 90-degree angles. Ninety-degree angles are also called right angles.

Question 2

The three angles inside a triangle add up to … The four angles inside any four sided figure add up to … A circle contains …. degrees Any line that extends from the center of a circle to the edge of a circle is called a …

Answer 2

The three angles inside a triangle add up to 180 degrees. The four angles inside any four sided figure add up to 360 degrees. A circle contains 360 degrees. Any line that extends from the center of a circle to the edge of a circle is called a radius.

Question 3

Vertical Angles

Answer 3

Vertical angles are the angles across from each other when two lines intersect. Vertical angles are always equal.

Question 4

Parallel Lines

Answer 4

Parallel lines never intersect. When a pair of parallel lines is intersected by a third, two types of angles are formed: big and small angles. Any big angle is equal to any big angle, and any small angle is equal to any small angle. The sum of any big and any small angle will always equal 180 degrees.

Question 5

Making assumptions

Answer 5

You need to be told that a drawing is something - e.g. actually parallel lines - instead of assuming.

Question 6

Triangles - Rule of 180º

Answer 6

Every triangle contains three angles that add up to 180º

Question 7

Triangles - Equilateral Triangles

Answer 7

An equilateral triangle is a triangle in which all three sides are equal in length. Because all three sides are equal, all of the angles are equal. Each angle = 60º

Question 8

Triangles - Isosceles Triangles

Answer 8

An isosceles triangle is a triangle in which two of the three sides are equal in length. That means two of the angles are equal.

Question 9

Triangles - Angle/Side Relationships

Answer 9

In any triangle the longest side is opposite the largest interior angle and vice versa. Equal sides are opposite equal angles.

Question 10

Triangles - Perimeter of a Triangles

Answer 10

Add up the perimeter of the triangle.

Question 11

Triangles - The Third Side Rule

Answer 11

The length of any one side of a triangle must be less than the sum of the other two sides and greater than the difference between the other two sides.

Question 12

Triangles - Area of a Triangle

Answer 12

A = 1/2 b*h

Question 13

Triangles - The Pythagorean Theorem

Answer 13

Applies only to right triangles. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of teh two other sides.

a²+b² = c²

Question 14

Triangles - Most Common Right Triangles

Answer 14

3, 4, 5

6, 8, 10

5, 12, 13

Question 15

Triangles - Right Isosceles Triangles

Answer 15

If you take a square and cut it in half along its diagonal, you will create a right isoceles triangle. 1 90º and 2 45º angles. The rations of the sides in a right isosceles triangle is:

x : x : x√2

Question 16

Triangles - 30 : 60 : 90 Triangles

Answer 16

If you take an equilaterial triangle and draw in the height, you create a right angle when you cut it in half.

The hypotenuse of the right tiangle has not changed. One of the 60 degree angles stays the same as well. The angle where the height meets the base is 90º, the angle opposite the smalest side is 30º.

The ratio of sides on a 30 : 60 : 90 triangle is x : x√3 : 2x

base : height : hypotenuse

Question 17

Four Sided Figures

Interior Angles

Area

Answer 17

Interior angles add up to 360 degrees

A = b*h

Question 18

Squares

Sides

Perimieter

Angles

Answer 18

Four equal sides

4x the length of any side

All 90º angles

A diagonal of the square splits it into two 45 : 45 : 90, or isosceles, right triangles.

Question 19

Circles

Radius

Chord

Diameter

Answer 19

Radius of a circle is any line that extends from the center of the circle to a point on the circumference of the circle.

Chord is a line that connects two pointss on the circumference of the circle.

Diameter is a line that connects two points on the circumference of the circle and that goes through the center of the circle.

Question 20

Circles - Circumference

Answer 20

circumference = 2πr or πd

Question 21

Circles - Arc and Central Angle

Answer 21

An arc is a section of the circumference ofa circle. An angle formed by two radii is called a central angle.

Question 22

Area of a Circle

Answer 22

area = πr²

Question 23

The Coordinate System

Answer 23

|
|
quadrant II | quadrant I

(-, +) | (+, +)

——————————————-|——————————————-

quadrant III | quadrant IV
(-, -) | (+, -)

|

Question 24

Slope

Answer 24

slope

y = mx + b On the GRE this may sometimes be written as

y = ax + b

X and y are both points on the line, b is the y-intercept, and m is the slope of the line

Slope = rise/run = (y₂ - y₁) / (x₂ - x₁)

Question 25

Volume of Three Dimensional Figures

Answer 25

Multiply the area of a two dimensional figure by its height. Rectangle - length x width x height

Cylinder - area of a circle x height

πr² h

Question 26

Diagonals in Three Dimensions

Answer 26

A special formula you cna use if you are ever asked to find the length ofa diagonal (the longest distance between any two corners) inside a three dimensional rectangular box.

a² + b² + c² = d²

a, b, c are the dimensions of the figure

Question 27

Surface Area of Rectangular Box

Answer 27

Sum of the areas of all its sides

Question 28

Draw it yourself if its not included

Redraw on tricky questions to eliminate answer choices and see if answer is (D)