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GMAT > Geometry > Flashcards

Geometry Flashcards

1
Q

Can you assume lines to be straight?

A

Yes

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2
Q

Can you assume lines to be perpendicular or parallel?

A

No

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3
Q

When are shapes congruent?

A

When they are of the same size and shape. Orientation does not matter.

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4
Q

If a line bisects a line and is perpendicular to it

A

Every point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.

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5
Q

Supplementary

A

180

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6
Q

Compelmentary

A

90

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7
Q

Sum of angles of a triangle

A

180

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8
Q

Acute angles

A

At least two of the angles in a triangle have to be acute

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9
Q

Largest angle always opposite

A

The longest side.

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10
Q

The sum of two sides of a triangle

A

Greater than the third side

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11
Q

The difference between the two sides of a triangle

A

Smaller than the third side

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12
Q

The third side

A

Greater than the difference and less than the sum

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13
Q

Can you assume that lines/angles that look similar or of the same length that they are?

A

No

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14
Q

Assuming for problem solving

A

Figure is always drawn to scale so we can assume that two angles are similar or close to one another by just looking at them; we can also assume the angle measurements; just visual ESTIMATION

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15
Q

Assuming for data sufficiency

A

Not always drawn to scale just use the information blatantly given to us

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16
Q

For all the diagrams

A

Look big and look small (specially for triangles)

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17
Q

Two way theorem-Isosceles triangle

A

Two angles opposite equal sides are equal

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18
Q

Equilateral triangle

A

Three equal 60 angles and three equal sides

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19
Q

Height

A

Segment from a vertex to the opposite side that is perpendicular*

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20
Q

Base

A

Whatever side the height is hitting

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21
Q

Right triangle area

A

Product of the two legs

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22
Q

All three sides can be used as a base but

A

They all give you the same area

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23
Q

Median

A

Line that goes from a vertex to the midpoint of the opposite side. Only divides that opposite side in half but does not divide the angle.

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24
Q

Angle bisector

A

Divides the angle in half but not the opposite side.

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25
In an isosceles and equilateral triangle
The line from the non equal angle to the opposite side= divides the angle into two equal angles, is perpendicular to the base, divides the base into half, if one segment is playing more than one role= isosceles; divides into two congruent right triangle;
26
Pythagorean triplet
3,4,5; 5,12,13; 8,15,17; 7,24,25; GCF times final answer
27
Congruent Shapes
Same shape and same size= basically equal
28
Similar shapes
Same shape but different sizes
29
Similar triangles
All angles are equal, (or know that two angles are equal
30
Similar triangles sides
Are proportional
31
In similar triangles
Any lengths are smaller triangle times scale factos
32
Similar triangles and the idea of scale factor
k
33
Area of similar triangles
Scaled up by ksquared
34
Halving and Doubling
Anything with 5 in the units digit double that and half the other one
35
45-45-90 triangle
1:1: root two; we get this when we divide a a square into two along one or both of its diagonals
36
30-60-90
1: root 3: 2
37
Area of an equilateral triangle
root 3 over four s squared
38
Sum of angles of a quadrilateral
360
39
Every quadrilateral, diagonals
Exactly two
40
Parellelogram
Opposite sides and angles are equal, sides are parellel, diagonals bisect each other; if any one of them is true all others are true
41
Rhombus
Diamond, four equal sides, they are parallelogram, + all four sides are equal and diagonals are perpendicular (these diagonal properties can be true for other irregular quads)
42
Rectangle
Special properties apart from the parallelogram: diagonals are congruent, not unique to rectangles
43
Square
Parallelogram; rhombus, and a square
44
Trapezoid
One set of parallel; if it is an isosceles trapezoid, then the non parallel sides are equal, opposite side angles are equal and diagonals are equal
45
Length of a slanted line
Pytha
46
Symmetrical trapezoid
Can divide into rectangle and two triangles on each side
47
Area of a rhombus and a paralellogram
B*H where h is the altitude
48
Area of a trapezoid
h * average of bases or divide it into two triangles and a rectangle**
49
Diagonals pentagons
Five
50
Hexagon diagonals
Nine
51
Sum of angles for polygons
(n-2)* 180
52
Regular polygon
Equal sides and equal angles; if a diagonal bisects the whole shape, it bisects the angle
53
Pie
22/7
54
Equal central angles
Equal arcs and equal chords
55
Inscribed Angle
Vertex on the circle, inscribed angle is half the central angle and the arc
56
If two different angles are drawn from the same chord
Then those two angles are equal; if they are on the same side of the chord
57
If an angle is drawn from two end points of a diameter
90 degree angle
58
Angle between radius and tangent point
90 degree
59
Trick
Find the chord
60
Space diagonal cuboid | one point to the opposite point of the other side
l squared + hsquared + b squared
61
Space diagonal cube
square root of 3 a
62
Cylinder volume and height
Volume= piersquaredh (base times height) | Surface area:2piersquared+ 2pierh
63
Sphere
Every point is equidistant from the center; volume= 4/3 piersquaredcubed Area: 4*pirsquared

GMAT (13 decks)

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