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GRE Quantitative > Geometry > Flashcards

Geometry Flashcards

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1
Q

Congruent

A

Equal

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2
Q

Midpoint

A

The point that divides a line segment into two congruent line segments

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3
Q

Opposite angles are…

A

congruent, have equal measures

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4
Q

Acute angle

A

less than 90 degrees

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5
Q

Obtuse angle

A

more than 90 degrees and less than 180

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6
Q

Z angles with parallel lines are…

A

equal (4 of 8 equal, other 4 are equal)

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7
Q

perimeter

A

the sum of the length of the sides

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8
Q

endpoints of a polygon are called…

A

vertices

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9
Q

if a polygon has n sides, it can be divided into…triangles

A

n-2

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10
Q

sum of interior angles of a polygon is…

A

(n-2)(180)

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11
Q

regular polygon

A

all sides and all interior angles are congruent

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12
Q

Characteristics of an equilateral triangle

A

all sides are equal

all angles equal 60

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13
Q

Characteristics of an isosceles triangle

A

two congruent sides (so two opposite equal angles)

third side is 180-2x

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14
Q

Pythagorean theorem

A

aˆ2 + bˆ2 = cˆ2

where c is the length of the hypotenuse

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15
Q

Lengths of sides in a 45-45-90 triangle

A

x, x, √2x

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16
Q

Lengths of sides of a 30-60-90 triangle

A

x, √3x, 2x

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17
Q

Area of a triangle

A

A = bh / 2
b=base
h=height

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18
Q

What conclusions can be drawn about congruency from the statement: “triangles PQR and STU are congruent”?

A

PQ and ST are same length
PR and SU are same length
QR and TU are same length
(And corresponding angles are also equal)

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19
Q

Congruent triangles

A

triangles with the same shape and size

20
Q

SSS congruence

A

Side-side-side congruence: if all three sides are congruent, the triangles are congruent

21
Q

SAS congruence

A

Side-angle-side congruence: If two sides and the angle between them are congruent, the triangles are congruent

22
Q

ASA congruence

A

Angle-side-angle congruence: If two angles and the side between them are congruent, the triangles are congruent

23
Q

Two ways to prove similar triangles

A
  1. corresponding angles are congruent

2. lengths of corresponding sides have same ratio (can set up proportions to calculate)

24
Q

Congruency in rectangles

A
  1. four right angles
  2. opposite sides are parallel and congruent
  3. two diagonals are congruent
25
Q

parallelogram

A

a quadrilateral in which both pairs of opposite sides are parallel
opposite sides are congruent
opposite angles are congruent

26
Q

trapezoid

A

at least one pair of opposite sides is parallel

the parallel sides are the bases

27
Q

area of a parallelogram (including squares and rectangles)

A

A = bh

28
Q

area of a trapezoid

A

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

29
Q

radius

A

distance from the center to an end

30
Q

diameter

A

2r

the distance across the circle going through the middle

31
Q

chord

A

any line segment joining two points on the circle

32
Q

formula for circumference

A

C = 2πr

33
Q

arc

A

the (outer) part of the circle containing two end points and all the points between them

34
Q

measure of an arc

A

the measure of its central angle

35
Q

length of an arc

A

length of arc / circumference (2πr) is proportionate to the central angle / 360

36
Q

area of a circle

A

πrˆ2

37
Q

area of a sector (piece) of circle

A

area of sector / area of circle (πrˆ2) is proportionate to central angle / 360

38
Q

tangent

A

a line that intersects a circle at exactly one point

39
Q

a radius drawn to a tangent is …. to the tangent line

A

perpendicular

40
Q

If all vertices of a polygon lie on a circle, the polygon is…
and the circle is…

A

inscribed in the circle

circumscribed about the polygon

41
Q

If one side of an inscribed triangle is the diameter of the circle, then the triangle is a…

A

right triangle

42
Q

volume of a rectangular solid

A

V = lwh

43
Q

surface area of a rectangular solid

A

A = 2(lw + lh + wh)

44
Q

volume of a right circular cylinder

A

V = πrˆ2h

45
Q

right circular cylinder

A

axis is perpendicular to its bases and the height is a perpendicular distance from both bases

46
Q

area of a right circular cylinder

A

A 2(πrˆ2) + 2πrh

47
Q

common Pythagorean triples

A 
3-4-5
6-8-10
5-12-13
10-24-26
12-16-20
7-24-25

GRE Quantitative (5 decks)

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