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GMAT > 003 FOM - Geometry > Flashcards

003 FOM - Geometry Flashcards

1
Q

What are vertical angles? What is true about them?

A

Opposite angles created when two straight lines intersect. They have the same measure.

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2
Q

Define a right angle.

A

An angle with the measure of 90 degrees.

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3
Q

How is a perpendicular line denoted?

A

By an upside down T.

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4
Q

Define a polygon.

A

A closed plane figure formed by three or more line segments (each a “side” of the polygon).

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5
Q

Define vertices.

A

The points of intersection on a polygon.

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6
Q

Define convex polygon.

A

Polygon where each interior angle has a measure of less than 180 degrees.

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7
Q

Define a quadrilateral

A

Polygon with four sides

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8
Q

Define a pentagon.

A

Polygon with five sides.

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9
Q

Define hexagon

A

Polygon with six sides.

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10
Q

Express the sum of the interior angles of a polygon as an equation.

A

180 degrees x (n-2)

Where n is the number of sides of the polygon.

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11
Q

Define isosceles triangle.

A

At least two sides of the triangle are of equal length.

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12
Q

What is true about sides/angles in an isosceles triangle?

A

If two sides are the same length, their opposite angles are the same length (and vice versa).

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13
Q

What are the components of a right triangle?

A

Sides forming right angle are LEGS. Third side opposite the right angle (and the longest side) is the HYPOTENUSE.

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14
Q

Define Pythagorean theorem.

A

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

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15
Q

Define right triangle

A

A triangle that has a right angle. Also any triangle in which the lengths of the sides are in the ratio 3:4:5.

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16
Q

What is the altitude of a triangle?

A

The segment drawn from a vertex perpendicular to the side opposite that vertex.

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17
Q

What is the base of a triangle?

A

Relative to a vertex and an altitude, the opposite side (ie the side where the altitude connects to). Any side of a triangle can serve as a base (whatever side the height is perpendicular to).

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18
Q

What is the area of a triangle?

A

(length of altitude * length of the base) / 2

aka, the average of the altitude and base

OR 1/2(base*height)

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19
Q

What is the ratio of sides in a 45-45-90 degree triangle?

A

1:1: sq root 2

In triangle JKL with hypotenuse KL, if JL =2 and JK = 2, then KL = 2sq rt 2

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20
Q

What is the ratio of sides in a 30-60-90 triangle?

A

1: sq rt 3: 2

For triangle XYZ with hypotenuse YZ, if XZ = 3, then XY = 3sqrt3 and YZ = 2X3=6

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21
Q

Define a line segment

A

A part of a line (i.e., a straight line that extends without end in both directions) between two endpoints on the line.

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22
Q

Define quadrilateral

A

Polygon with four sides

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23
Q

Define parallelogram

A

Quadrilateral in which both pairs of opposite sides are parallel and equal.

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24
Q

Define rectangle vs. square

A

Parallelogram with right angles. Square is a rectangle with all sides of equal length.

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25
Q

Define trapezoid

A

Quadrilateral with two sides parallel. Third and fourth sides are slightly diagonal.

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26
Q

What is the area of a trapezoid?

A

(1/2)(sum of the lengths of the bases)(the height)

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27
Q

Define a circle

A

Set of points in a plane that are located the same distance from a fixed point (the center of the circle).

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28
Q

Define chord in the context of a circle.

A

Line segment that has its endpoints on the circle.

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29
Q

Define diameter.

A

A chord that passes through the center of the circle.

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30
Q

Define radius

A

Segment from the center of the circle to a point on the circle. Equals one-half of the diameter.

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31
Q

Define circumference of a circle.

A

The perimeter of the circle. Defined as 2pir, where pi is approximately 3.14, and r is the radius.

32
Q

Define area of a circle

A

pi*r^2 where pi is about 3.14 and r is the radius

33
Q

How to find the length of an arc in a circle?

A

(x/360) where x is the degrees of the angle formed by the two radii that form the boundaries of the arc.

34
Q

What is a tangent line in relation to a circle?

A

A line with one point in common with a circle (ie the point of tangency).

35
Q

Define inscribed.

A

Being contained within something else.

36
Q

Define circumscribed

A

Containing something else.

37
Q

Relate right triangles to circles.

A

One of the sides of a right triangle that is inscribed in a circle will be the diameter of the circle.

38
Q

What is a rectangular solid?

A

A 3D figure formed by 6 rectangular surfaces, each a face. Has 6 faces, 12 edges, and 8 vertices.

39
Q

What is the surface area of a rectangular solid?

A

Sum of all the areas of the faces.

40
Q

What is the volume of a rectangular solid?

A

Length x width x height

aka: area of the base x height

41
Q

What is the surface area of a cylinder?

A

2(pir^2) + 2pirh

aka the sum of the areas of the two bases, plus the area of the curved surface

42
Q

What is the area of a cylinder?

A

pir^2h

aka the area of the base x the height

43
Q

What is the x axis?

A

The horizontal line on a coordinate plane

44
Q

What is the origin?

A

Where the x and y axes intersect on a coordinate plane.

45
Q

What are the divisions of a plane called?

A

Quadrants

46
Q

Express a point on the coordinate plane

A

(x,y)

47
Q

How to find the distance between two points on a plane?

A

Pythagorean theorum using a right triangle where the two points are two endpoints of a hypothetical triangle, with the straight line between the two serving as the hypotenuse of the triangle.

48
Q

What is the equation of a line on a plane? A vertical line? Define the terms

A

y = mx + b where m is the slope, and constant term b is the y-intercept

vertical line: x=a

49
Q

What is the slope of a line?

A

(difference in y coordinates)/(difference in x coordinates)

i.e., rise/run

50
Q

How do you find the x intercept of a line?

A

Set y = 0 and solve for x in the equation y=mx+b

51
Q

What is true about a circle?

A

If you know one thing about it (radius, diameter, circumference, area), you can determine everything else.

d = 2r; c = 2pir (aka dpi); a = pi*r^2

52
Q

Define the relationship between circumference and diameter.

A

c = d*pi, therefore c/d = pi

53
Q

Define sector

A

A fractional portion of the circle (slice of pizza).

54
Q

Define arc length

A

The portion of the circle’s arc that is bound by a sector.

55
Q

Define central angle.

A

A measure of the degrees between two radii, which make up the outer bounds of a circle’s sector.

56
Q

What is the formula for area of a sector?

A

Area of the circle * (central angle/360)

57
Q

What is the formula for arc length of a sector?

A

2pi*r x (central angle/360)

58
Q

What is true about the sides of a triangle a, b and c?

A

1) The sum of a + b > c.

2) The difference of a-b

59
Q

What is true about the interior angles of a triangle?

A

They add up to 180 degrees

60
Q

What is true about the GMAT and geometrical shapes?

A

They are not always drawn to scale!

61
Q

What is the relationship between a triangle’s interior angles and the length of its sides?

A

The longest side is opposite the largest angle.

62
Q

What is true about the height of a triangle?

A

It can be outside the triangle - just extend the base.

63
Q

Define hypotenuse.

A

The side of a triangle opposite the right angle.

64
Q

What are the sides of a right triangle besides the hypotenuse called?

A

The legs.

65
Q

Define Pythagorean triplet.

A

A right triangle in which all three sides have lengths that are integers.

66
Q

Name the 5 most common Pythagorean triplets.

A

3-4-5 (and doubled, 6-8-10)

5-12-13 (and doubled, 10-24-26)

8-15-17

67
Q

What is true about Pythagorean triplets?

A

You can scale them in size by applying a common multiplier.

68
Q

What is true about splitting quadrilateral shapes?

A

You can always split them into two triangles.

69
Q

What do hash marks in a shape signify?

A

Equal lengths or angles.

70
Q

What do arrows in shapes signify?

A

Parallel lines

71
Q

How do you find the area of a parallelogram?

A

Base x height

72
Q

What is true about the interior angles of a parallelogram?

A

Opposite angles are also equal, and adjacent angles add up to 180 degrees.

73
Q

What’s the difference between a line and a plane?

A

A line is one-dimensional, because you only need one number to identify a point’s location. A plane is two-dimensional because you need two numbers to identify a point’s location.

74
Q

What should you do if you know just one coordinate?

A

Narrow down the possibilities by drawing a line

75
Q

What are the quadrants of a coordinate plane.

A

1-4 going clockwise, with 1 in the upper right-hand corner.

76
Q

What does y = 2x+4 indicate?

A

The line crosses the y-intercept at +4. The line slopes up and to the right, with two increases in y (rise) for every increase in x (run)

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