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geometry > final > Flashcards

final Flashcards

1
Q

what is a triangle?

A

a closed figure in a plane consisting of 3 segments called sides

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2
Q

how are triangles named?

A

using the capital letters assigned to its vertices in a clockwise or counterclockwise direction

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3
Q

what are the properties of a scalene triangle?

A

no sides are congruent and no angles are congruent

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4
Q

what are the properties of a isosceles triangle?

A

at least two sides are congruent and two angles called the base angles are congruent

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5
Q

what are the properties of an equilateral triangle?

A

all three sides are congruent and all three angles are congruent

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5
Q

what are the properties of a right triangle?(op)

A

-exactly one angle is a right angle
-the acute angles are complementary
-the side opposite the right angle called the hypotenuse is the longest side

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6
Q

what are the properties of an acute triangle?(op)

A
  • all three angles are acute
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7
Q

what are the properties of an obtuse triangle?(op)

A

exactly one angle is an obtuse angle

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8
Q

what is the triangle-angle sum theorem

A

m<A+m<B+m<C=180°

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9
Q

what is the exterior angle theorem?

A

m<1=m<A+m<B

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10
Q

what is the pythagorean theorem?

A

c^2=a^2+b^2

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11
Q

what is the hypotenuse and what is its notation

A

the side opposite the right angle in a right angled triangle
often denoted as ‘c’

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12
Q

what are the legs and what are their notation

A

the two shorter sides that form the right angle
often denoted as ‘a’ an ‘b’

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13
Q

what is the converse of the pythagorean theorem?

A

if the sum of the measure of the two legs of a triangle equals the square of the measure of the longest side then the triangle is a right triangle

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14
Q

if c^2<a^2+b^2 then the triangle is

A

an acute triangle

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14
Q

what is a radius

A

a line segment from the center to a point on the circle

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15
Q

if c^2=a^2+b^2 then the triangle is

A

a right triangle

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15
Q

if c^2>a^2+b^2 the the triangle is

A

an obtuse triangle

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15
Q

what is a circle

A

a set of all point in a plane that are the same distance from a given point called the center of the circle

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16
Q

what is a chord

A

a segment with endpoints on the circle

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17
Q

what is a diameter

A

a chord that passes through the center of the circle

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18
Q

what is the circumference

A

the distance around the circle

19
Q

what is the formula for diameter

A

d=2xr

19
Q

what is the formula for the radius

A

r=d/2

19
Q

what is the formula for circumference

A

c=2πr

20
Q

what is a central angle of a circle

A

an angle with a vertex at the center of the circle and sides that are radii

21
Q

what is the formula to get the sum of the central angles

A

m<1+m<2+m<3=360°

22
Q

a minor arc has a measure of

A

less than 180°

23
Q

what is an arc

A

part of a circle that is defined by two endpoints

23
Q

a major arc has a measure of

A

more than 180°

24
Q

a semicircle has a measure of

A

exactly 180°

25
Q

what is the arc length

A

the distance between the endpoints of an arc measured along the arc in linear units.

25
Q

what are congruent arcs

A

arcs that have the same measure

26
Q

what are adjacent arcs

A

arcs that have exactly one point in common

27
Q

what is the formula to find the length

A

l= x/360 x 2πr

28
Q

what is a radian

A

a unit of angular measurement equal to 180°/π

29
Q

degree –> radians

A

π radians/ 180°

30
Q

radians –> degree

A

180°/ π radians

31
Q

what is a quadrilateral

A

four sided figure

32
Q

what is the area

A

the space inside the shape

32
Q

what is a rectangle

A

a quadrilateral with both pairs of opposite sides parallel and equal and four right angles

32
Q

what is a square

A

a quadrilateral with 4 equal sides and 4 right angles the opposite sides in a square are both parallel and equal in length

33
Q

how to find the area of a square

A

A= a^2

34
Q

how to find the area of a rectangle

A

a=lxw

35
Q

how to find the area of a parallelogram

A

a=bxh

35
Q

what is the base of a parallelogram

A

any side of the parallelogram

36
Q

what is a parallelogram

A

quadrilateral with both pairs of opposite sides parallel and equal(2 pairs of parallel sides)

37
Q

what is the height of a parallelogram

A

the length of the altitude(perpendicular) of the parallelogram

38
Q

what is a trapezoid

A

a quadrilateral with exactly one pair of parallel sides(1 pair of parallel sides)

38
Q

how to find the area of a trapezoid

A

A= 1/2 h (b1+b2)

38
Q

what is a kite

A

a quadrilateral with exactly 2 pairs of consecutive congruent sides(2 consecutive equal sides)

39
Q

what is a rhombus

A

a parallelogram with all four sides congruent(2 pairs of parallel sides, all sides are congruent)

40
Q

what is the area of a kite/rhombus

A

a=1/2(d1d2)

41
Q
A

geometry (6 decks)

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