Gmat Assignment 5

Front 1

Geometry Problem solving

Back 1

You can trust what you see. Figures are drawn to scare unless a problem states otherwise.

Front 2

Geometry Data Sufficiency

Back 2

Be wary of what you see. Figures are not necessarily drawn to scale, and they may be drawn inaccurately in order to confuse you.

Front 3

Geometry Transcription

Back 3

Make sure you have correctly transcribed the diagram before you begin solving a problem. If no diagram is provided, draw one yourself.

Front 4

Lines & Angles

Back 4

Two points determine a line.

Angle are measured in degrees, and a complete circle contains 360°. A straight line contains 180°.

Front 5

Intersecting Lines

Back 5

When two straight lines intersect, the angles opposite each other are equal. These are called vertical angles or opposite angles.

Front 6

Perpendicular Lines

Back 6

An angle of 90° is a right angle. two lines that meet at a right angle are perpendicular, indicated by the ⊥ symbol.

Front 7

Parallel Lines

Back 7

If two lines in a plane never intersect, they are parallel, denoted by the symbol ∥.

Front 8

Line crossing parallel line

Back 8

Two kind of angle are formed: big angles and small angles.

All big angles are equal, and all small angles are equal.

Any big angle plus any small angle equals 180°.

Front 9

Parallelograms

Back 9

Four-sided figures made up of two pairs of parallel lines.

The opposite big angles are equal, the opposite small angles are equal. and the sum of any big angle and small angle is 180°.

Front 10

Triangles

Back 10

A three-sided figure with three corresponding angles.

The points where the sides meet are called vertices (each corner is called a vertex).

Perimeter is sum of lengths of its sides.

Front 11

Triangles & Angle relationships

Back 11

In any triangle, larger sides are opposite larger angles.

Smaller sides are opposite smaller angles.

Equal sides are opposite equal angles.

Front 12

Area of Triangle

Back 12

A= 1/2bh

Any side of triangle can serve as the base.

Key is to remember that the height must be perpendicular to the base.

Front 13

Equilateral triangles

Back 13

Have three equal sides and three equal angles @ 60°.

Front 14

Isosceles Triangles

Back 14

Have two equal sides, and the two angles opposite those sides are also equal.

Front 15

Right triangles

Back 15

Contain one right 90° angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called the legs.

Front 16

Impossible triangles

Back 16

The length of any 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.

Front 17

Quadrilaterals

Back 17

A four-sided figure. Has 360°.

Front 18

Parallelograms

Back 18

Opposite sides are equal and parallel.

Opposite angles are equal.

Adjacent angles add up to 180° (big angle + small angle = 180°)

Area = bh (height must be perpendicular to the base)

Front 19

Rectangles

Back 19

Parallelogram with four right angles.

Area = lw

Perimeter = 2(l + w) or 2l + 2w

Front 20

Squares

Back 20

Area = s^2

Perimeter = 4s

Front 21

Circles - Radius

Back 21

The distance from the center of the circle out to the edge. All radii are equal.

Front 22

Circles - Chord

Back 22

A line segment from one point on the circle to another.

A chord that passes through the center of the circle is called a diameter.

The diameter is the longest chord in the circle. d = 2r

Front 23

Circle - Circumference

Back 23

The distance around a circle.

Circumference = πd or 2πr

Front 24

Circle - Arc

Back 24

A piece of a circle (a portion of the circumference)

Front 25

Circle - π

Back 25

Relationship between the circumference of any circle and its diameter.

Circumference is π times the diameter.

Front 26

Circle - Area

Back 26

Area = πr^2

Front 27

Circle - Central Angle

Back 27

If x is measure of central angle, the length of arc is x/360 times the circumference of entire circle and the area of a sector is x/360 times the area of the entire circle.

Front 28

Coordinate Geometry

Back 28

Horizontal x-axis; Vertical y-axis

Origin is the intersection of the axes and has the coordinates (0,0).

A line that rises from left to right has a positive slope.

A line that falls from left to right has a negative slope.

A horizontal line has a slope of 0.

Front 29

Solid Geometry

Back 29

Rectangular solid v = lwh

Cube v = s^3

Cylinder v = πr^2h

Surface area is the combined area of all the surfaces of a solid.

Front 30

Types of right triangles

Back 30

3-4-5

6-8-10
5-12-13

Front 31

45:45:90

Back 31

x,x, x√2

2, 2, 2√2

Front 32

30:60:90

Back 32

x,x√3, 2x

5, 5√3,10

Front 33

y = mx + b

Back 33

x and y are coordinates

m is the slope

b is the point (0,b) where the line crosses the y-axis

Front 34

Area of Equilateral Triangle

Back 34

s^2√3
---------
4

Front 35

Diagonal formula

Back 35

a^2 + b^2 + c^2 = d^2

Front 36

Surface area of a box

Back 36

2 lw + 2 lh + 2 hw