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GRE Math > Geometry > Flashcards

Geometry Flashcards

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1
Q

vertices (polygons)

A

endpoints of the sides that meet

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2
Q

how many triangles can a polygon be divided into

A

n-number of sides

n-2

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3
Q

how to find sum of interior angles of a polygon

A

(n-2)(180º)

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4
Q

Regular polygon

A

all sides and all angles are congruent

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5
Q

How to find the angles of a regular polygon when you know the sides

A

(n-2)(180) = x

x/n = degree of each angle

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6
Q

Triangles

A

sum of interior angles = 180º

length of each side is less than the sum of the other 2 sides

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7
Q

equilateral triangle

A

3 congruent sides

3 congruent angles (60°)

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8
Q

isosceles triangle

A

2 congruent sides

angles opposite the congruent sides are congruent

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9
Q

right triangle

A

has interior right angle

hypotenuse is the side opposite the right angle

other sides are legs

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10
Q

Pythagorean theorem

A

hypotenuse2 = leg12 + leg22

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11
Q

ratio of sides of an isosceles right triangle

A

1 : 1: √2

y2 = x2 + x2

y2 = 2x2

y = √2x

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12
Q

30° 60° 90° triangle

A

half of an equilateral triangle

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13
Q

ratio of sides of a 30-60-90 triangle

A

1: √3: 2

x2 + y2 = (2x)2

x2 + y2 = 4x2

y2 = 3x2

y = √3x

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14
Q

Area of triangle

A

A = (bh)/2

base x height

  • any side can be the base
  • height is a perpendicular line from base to opposite vertex
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15
Q

3 ways to tell if two triangles are congruent

A
  1. if 3 sides of one triangle are congruent to the other
  2. if 2 sides and its angle are congruent on each
  3. if 2 angles and a side are congruent
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16
Q

similar triangles

A

same shapes but not necessarily the same size

you can match up the vertices so the angles are congruent

OR

the lengths of corresponding sides have the same ratio

(all 30-60-90° triangles are similar)

17
Q

proportions of similar triangles ABC and DEF

A

AB = BC = AC

DE = EF = DF

18
Q

sum of interior angles of a quadrilateral

A

360°

19
Q

rectangles

A

4 right angles

opposite sides are parallel and congruent

2 interior diagonals are congruent

if all four sides are congruent its a square

20
Q

parallelogram

A

both pairs of opposite sides are parallel

opposite sides are congruent and opposite angles are congruent

21
Q

trapezoid

A

2 opposite sides are parallel

A = 1/2 (b1 + b2)(h)

bs are corresponding sides

22
Q

Area of all parallelograms

A

A=bh

any side can be base

height is perpendicular line reaching to the other side

23
Q

Diameter =

A

2r

radii

24
Q

radii of congruent circles

A

equal radii

25
Q

chord

A

any line segment joining to points on the circle

26
Q

circumference

A

distance around the circle

C/d = π

or

C = dπ

or

C = 2πr

27
Q

finding the length of an arc on a circle

A

ratio of arc length to circumference are the same as the ratio of inner arc degree to 360°

length of arc ABC = arc°

circumference = 360°

28
Q

Area of a circle

A

πr2

29
Q

tangent

A

line that intersects a circle at exactly one point

radius is perpendicular to tangent lines

30
Q

rule about triangles inscribed in circles

A

if one side of an inscribed triangle is a diameter of the circle then the triangle is a right triangle

(vice versa: a right triangle inscribed inside of circle then one side of it is the diameter)

31
Q

rectangular solids

A

6 faces

12 edges

8 vertices

32
Q

volume of rectangular solid

A

V = l x w x h

33
Q

surface area of a rectangular solid

A

sum of face areas

A = 2 (lw + lh + wh)

34
Q

cube

A

6 square faces

l = w = h

35
Q

Axis of cylinder

A

line that joins the 2 centers of the circles (its height)

36
Q

right circular cylinder

A

axis is perpendicular to bases

37
Q

volume of cylinder

A

V = πr2h

38
Q

Surface area of cylinder

A

(2πr2) + 2πrh

GRE Math (5 decks)

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