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GRE 2017 > Geometry > Flashcards

Flashcards in Geometry Deck (32):
1

Bisecting line` `

Splits something into 2 EQUAL parts`

2

Be aware that polygons do not have to...

...be "regular."

Regular = all sides the same lengt

3

Sum of interior angles of a triangle

Add up to 180

4

Sum of interior angles of a quadrilateral (4 sides)

Add up to 360

5

The sum of the interior angles of every pentagon (5 sides)

Add up to 540

6

Hexagon - sum of interior angles...

...add up to 720

7

Sum of interior angles of any polygon =

(n-2)180

8

Sum of exterior angle and interior angle...

...always equals 180

9

Num of interior angles and exterior angles in every polygon

Is equal (triangle has 3 interior angles, that add up to 180, and 3 exterior angles)

10

The sum of the exterior angles of ANY polygon...

...is always equal to 360

11

For triangles - an EXTERIOR angle of a triangle is always equal to....

...the SUM Of the NON-ADJACENT interior angles.

12

Never assume...

...that the lines are parallel, angle is right, shape is a square, etc. (Unless the exam explicitly states otherwise)

13

Tricky problem with lines and angles...

1. Draw the diagram
2. Look for relationships you know
3. Don't be afraid to "tune out" lines temporarily
4. If you can find >1 equation , COMBINE equations using subtraction or elimination
5. Look back at the diagram to see if your solutions make sense with the general shape

14

180-x trick

Label ALL of the interior (or exterior) angles of the polygon, using 180-x

15

Isosceles

2 angles of = measure, 2 sides of = measure.

NOTE - an equilateral is just a SPECIAL type of isosceles.

16

Pythagorean triples

3-4-5 (6-8-10; 9-12-15; 12-16-20; 15-20-25)
5-12-13 (10-24-26)
8-15-17
7-24-25

17

45-45-90 triangles [isosceles right triangle]

x:x:x(sq.rt of 2)

18

45-45-90 Short-Cut

CUT the hypothenuse in HALF and MULTIPLY the result by sq. root of 2

19

Every equilateral triangle

Is composed of TWO 30-60-90 triangles

20

Perimeter and triangle inequality theorem

Sum of any two sides of any triangle must be greater than the third side. Conversely, the difference of any two sides must be less than the third.

LESS THAN THE SUM, BUT GREATER THAN THE DIFFERENCE

21

Parallelogram - adjacent angles

Always add up to 180

22

Diagonals of a parallelogram...

...bisect one another and split the shape into two equilateral triangles

23

Area of a parallelogram

Is equal to BASE times HEIGHT

24

Area of a trapezoid

Average of bases x height

25

Units in a surface area question...

...should be squared

26

Volume of a rectangular solid

Length x Width x Height

27

Units when calculating volumen...

Should be cubed

28

How to determine the interior diagonal of a rectangular slid?

The Diagonal of a Rectangular Solid = square root of (lˆ2 + wˆ2 + hˆ2)

29

Diagonal of a Cube

Diagonal of a Cube = s (square root of 3)

S = side length

30

To find the midpoint if you know the two coordinates

Average the x-coordinates and y-coordinates

31

Perpendicular lines

The product of their slopes = -1

32

Surface area of a rectangular solid = ?

2(lw + wh + lh)