Geometry Flashcards Preview

GMAT Quantitative > Geometry > Flashcards

Flashcards in Geometry Deck (47):
1

Triangles Perimeter

P = A + B + C

2

Triangle Area

A = (B×H) ÷ 2

3

Specific triangles

30-60-30 = 1:sqrt(3):2 - 45-45-90 = 1:1:sqrt(2)

4

Square properties

All opposites sides are parallel and have the same length. All angles are 90°. Diagonal have the same length, intersect at 90° and bisect each other. Interior angles add up to 360°.

5

Square area

A = s2

6

Square perimeter

P = 4s

7

Square key shapes

Diagonals create two 45-45-90 isoceles right triangles.

8

Rectangle properties

All opposites sides are parallel. Opposite sides are the same length. All angles are 90°. Diagonals are the same length and bisect each other. Interior angles add up to 360°.

9

Rectangle area

A = l × w

10

Rectangle perimeter

P = 2l + 2w

11

Rectangle key shapes

Diagonals create 2 right triangles.

12

Parallelogram properties

All opposites sides are parallel. Opposite sides are the same length. Opposite angles are equal. Diagonals bisect each other. Interior angles add up to 360°.

13

Parallelogram area

A = b × h

14

Parallelogram perimeter

P = 2a + 2b

15

Parallelogram key shapes

Right triangle needed to find the height.

16

Trapezoid properties

2 sides are parallel. Interior angles add up to 360°.

17

Trapezoid area

A = 1/2 (b+c)h with b and c the length of the parallel sides.

18

Trapezoid perimeter

P = a + b + c + d

19

Trapezoid key shapes

Right triangle needed to find the height.

20

Sum of angles of a polygon

SoA = (n-2)×180 (with n the number of sides)

21

Circle area

A = πr^2

22

Circle circumference

C = 2πr

23

Circle arc length

AL = 2πr ( x/360 ) with x the central angle measure

24

Circle - Similar inscribed angles

All inscribed angles that extend to the same arc or same two points on a circle are equal.

25

Circle - Central angle x vs. inscribed angle y

Any central angle that extends to the same arc or same two points on a circle as does an inscribed angle is twice the size of the inscribed angle. x = 2y

26

Circle - Triangles inscribed in a semicircle

Any triangle inscribed in a semicircle with the circle diameter as longer side is always a right triangle.

27

3D figures - Volume

V = (area of 2-D surface)×h

28

Cube volume

V = s3

29

Cube surface area

SA = 6s2

30

Cube longest length within

L = sqrt(3s^2)

31

Rectangular solid volume

V = lwh

32

Rectangular solid surface area

SA = 2lw + 2lh + 2hw

33

Rectangular solid longest length within

L = sqrt( l^2 + w^2 + h^2 )

34

Cylinder volume

V = π×r^2×h

35

Cylinder surface area

SA = 2(πr^2) + 2πrh

36

Cylinder longest length within

L = sqrt(4r^2 + h^2)

37

Cylinder longest length within

L = sqrt(4r^2 + h^2)

38

Cylinder longest length within

L = sqrt(4r^2 + h^2)

39

Sphere volume

V = (4/3)πr^3

40

Sphere surface area

SA = 4πr^2

41

Sphere longest length within

L = 2r

42

Slope intercept formula

y = mx + b with m the slope, b the y-intercept and (-b/m) the x-intercept.

43

Slope of a line

Δy / Δx = (y2 - y1) / (x2 - x1)

44

x- and y-intercepts

1 - Use y = mx + b formula. 2 - Set x equal to 0 to find the y-intercept. Set y equal to 0 to find the x-intercept.

45

Calculating intersections of two lines

Set both equations equal to each other and resolve. (l1) : y=ax+b ; (l2) : y=mx+p --> ax+b=mx+p

46

Distance between any two points

(p1) : (x1, y1) ; (p2) : (x2, y2) --> d(p1, p2) = sqrt( (Δx)^2 + (Δy)^2 ) = sqrt( (x1-x2)^2 + (y1-y2)^2 )

47

Midpoint formula

(p1) : (x1, y1) ; (p2) : (x2, y2) --> Midpoint = ( (x1+x2)/2, (y1+y2)/2 )