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Geometry > Geometry Basics Chapter 1-2 > Flashcards

Geometry Basics Chapter 1-2 Flashcards

1
Q

Altitude to a side of a triangle

A

A segment from a vertex perpendicular to the opposite side

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1
Q

How many lines can be drawn through any two points?

A

One and only one

AB is the only line that can be drawn between A and B

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2
Q

Right Angle

A

An angle that measures 90 degrees

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2
Q

Right Triangle

A

A triangle having a right angle

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2
Q

Postulate 9: Powers Postulate

A

Like powers of equals are equal.

If a=b then a squared=b squared

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3
Q

Principle of Pairs of Angles: If angle of c degree is cut into two adjacent angles of a degree and b degree…

A

then a degree+b degree=c degree

Principle of Pairs of Angles

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3
Q

Hypotenuse

A

The longest side of a triangle

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3
Q

How many bisectors are in an angle?

A

One and only one

Only AD is the bisector of angle A

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4
Q

True/False: A geometric figure can be moved without change in size or shape?

A

True

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5
Q

If a Line Segment is divided into two equal parts

A

The point of division is the midpoint of the line segment

The line that crosses at the midpoint is said to bisect the segment

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6
Q

Complementary Angles

A

Complementary Angles are two angles whose measure total 90 degrees

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6
Q

If a line segment is divided into parts

A

The length of the whole line segment equals the sum of the length of its parts.

The length of the whole line segment is greater than the length of any part

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6
Q

Perpendicular

A

Lines, rays, or segments that meet at right angles.

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6
Q

Isosceles Triangle

A

A triangle having at least two congruent sides

The equal sides are called the legs

The remaining side is called the base

Angles on either side of the base are base angles

Angle opposite the base is the vertex angle

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6
Q

Postulate 4: Reflexive Postulate or Identity Postulate

A

Any quantity equals itself

X=X, AB=AB, angle A=angle A

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7
Q

Angle

A

An angle is the figure formed by two rays with a common end point. The rays are the sides of the angle, while the end point is its vertex.

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8
Q

Postulate 2: Substitution Postulate

A

A quantity may be substituted for its equal in any expression or equation.

If x=5 and y=x+3, we may substitute 5 for x and find y=5+3=8

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9
Q

Scalene Triangle

A

A triangle having no congruent sides

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10
Q

Central Angle

A

An angle formed by two radii

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11
Q

All Vertical angles

A

Are Congruent

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12
Q

Chord

A

A segment joining any two points on a circle

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14
Q

Point

A

Point has position only. It has no length, width, or thickness. A point is represented by a dot. A point is designated by a capital letter next to the dot.

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14
Q

Postulate 13: The length of a segment is the…

A

Shortest distance between two points

AB is shorter than the curved or broken line segment between A and B

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14
Q

Theorem

A

A statement, which when proved, can be used to prove other statements or derive other results. Each basic theorems requires the use of definitions and postulates for its proof.

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16
Q

Radius

A

A segment joining the center of a circle to a point on the circle.

The def of a circle, it follows that the radii of a circle are congruent.

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17
Q

Postulate 16: How many midpoints are on a given segment?

A

One and only one

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18
Q

Quadrilateral

A

A polygon having four sides

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19
Q

Postulate 14: How many circles can be drawn with any given point as center and a given line segment as a radius?

A

one and only one circle

only circle A can be drawn with A as center and AB as a radius

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21
Q

Adjacent Angles

A

Two angles that share the same vertex and have a common side between them.

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22
Q

Altitudes of obtuse triangle

A

Altitude drawn to either side of the obtuse angle fall outside the triangle

Thus in obtuse triangle ABC (shaded), altitudes BD and CE fall outside the triangle. In each case, a side of the obtuse angle must be extended

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23
Q

Plane Surface

A

A plane surface is a surface such that a straight line connecting any two of its points lies entirely in it. A plane is a flat surface.

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24
Q

Angle Bisector of a triangle

A

A segment or ray that bisects an angle and extends to the opposite side

BD the angle bisector of angle B, Bisects angle B making angles 1 and 2 congruent.

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24
Q

Median of a Triangle

A

A segment from a vertex to the midpoint of the opposite side

BM, the median to AC, bisects AC, making AM=MC

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26
Q

What does it mean to have supplementary angles that are congruent?

A

Each of the angles is a right angle

27
Q

Diameter

A

A diameter is a chord through the center of the circle

The longest chord

Twice the length of the radius

27
Q

Obtuse Angle

A

An angle whose measure is more than 90 degrees and less than 180 degrees.

28
Q

Straight Line

A

are unlimited in extent and may extend in either direction infinetly.

29
Q

Surface

A

A surface has length and width but no thickness.

31
Q

Congruent Angles

A

Angles that have the same number of degrees

32
Q

When are adjacent angles supplementary?

A

If their exterior sides lie in the same straight line

33
Q

What is the distance around the circle?

A

The Circumference (360 degrees)

34
Q

Pentagon

A

A polygon of five sides

35
Q

Obtuse triangle

A

A triangle having an obtuse angle

36
Q

Perpendicular bisector of a side

A

A line that bisects and is perpendicular to a side

PQ, the perpendicular bisector of AC, bisects AC and is perpendicular to it

37
Q

Particular Statement

A

Statement about one or some of the members of the set or class referred to in the general statement: All greyhounds are dogs.

39
Q

If two supplementary angles contain a degree and b degree…

A

Then a degree + b degree = 180 degree

40
Q

Postulate 10: Roots Postulate

A

Like roots of equals are equal

41
Q

Straight Angle

A

An angle that measures 180 degrees

42
Q

Postulate 5: Addition Postulate

A

If equals are added to equals, the sums are equal

if a=b and c=d then a+c=b+d

42
Q

Postulate 6: Subtraction Postulate

A

If equals are subtracted from equals, the differences are equal

if a=b and c=d, then a-c=b-d

44
Q

Supplementary Angles

A

Supplementary Angles are two angles whose measures total 180 degrees

45
Q

Postulate 18: Through any point on a line, how many perpendiculars can be drawn to the line?

A

One and only one

Only PC is perpendicular to AB at point P on AB

46
Q

Postulate 1: Transistive Postulate

A

Things equal to the same or equal things are equal to each other

If a=b and c=b, then a=c

48
Q

If two complementary angles contain a degree and b degree

A

then a degree + b degree = 90 degrees

Principles of Pairs of Angles

50
Q

Supplements of the same angle are…

A

Congruent

angle a is congruent to angle b and each is the supplement of angle x

51
Q

Postulate 3: Partition Postulate

A

The whole equals the sum of its parts

the total value of a dime, a nickel, and a penny is 16 cents

53
Q

Equilateral Triangle

A

A triangle having three congruent sides

AKA an isoceles triangle

55
Q

Arc

A

An arc is a continuous part of a circle.

56
Q

Deduction

A

Follows logically when the general statement is applied to the particular statement: All greyhounds are quadrupeds

57
Q

All straight angles are…

A

Congruent

59
Q

Vertical Angles

A

Vertical angles are two non adjacent angles formed by two intersecting lines

60
Q

Complements of congruent angles are….

A

Congruent

angle c is congruent to angle d and their complements are the congruent angles x and y

61
Q

Acute Angle

A

An acute angle is an angle whose measure is less than 90 degrees.

62
Q

Acute Triangle

A

A triangle having three acute angles

63
Q

General Statement

A

referring to a whole set or class of things, such as the class of dogs: All dogs are quadrupeds

64
Q

Ray

A

Ray is the part of a straight line beginning at a given point and extending limitlessly in one direction.

65
Q

A line that bisects an angle

A

Divides it into two congruent parts

66
Q

Postulate 8: Division Postulate

A

If Equals are divided by equals, the quotients are equal

if a=b and c=d, then a/c=b/d

67
Q

True or False: Vertical angles are not congruent

A

False

angle a= angle b; this follows principle 4 (supplements of the same angle are congruent), since angle a and angle b are supplements of the same angle, angle c

68
Q

How many points can two lines intersect?

A

One and only one point

Only P is the point of intersection of AB and CD

69
Q

Polygon

A

A closed plane figure bounded by straight line segments as sides

70
Q

Semicircle

A

An arc measuring one-half of the circumference of a circle and thus contains 180 degrees.

(a diameter divides a circle into two semicircles)

72
Q

Line

A

A line has length but has no width or thickness.

A line may be straight, curved, or a combination of these.

73
Q

Circle

A

A circle is the set of all points in a plane that are the same distance from the center.

74
Q

Supplements of congruent angles are…

A

Congruent

angle c is congruent to angle d and their supplements are the congruent angles x and y.

75
Q

Triangle

A

A polygon having three sides whose degrees allways measure 180.

76
Q

When are Adjacent angles complementary ?

A

If their exterior sides are perpendicular

77
Q

Vertex of a triangle

A

A point at which two of the sides of the triangle meet

78
Q

Compliments of the same angle are….

A

Congruent

angle a is congruent to angle b and each is the compliment of angle x

80
Q

Through any point outside a line, how many perpendiculars can be drawn to a given line?

A

One and only one

81
Q

All right angles are….

A

Congruent

82
Q

Postulate 7: Multiplication Postulate

A

If equals are multiplied by equals, the products are equal;

if a=b and c=d, then ac=bd

83
Q

Perpendicular Bisector

A

A perpendicular bisector of a given segment is perpendicular to the segment and bisects it.

84
Q

What does it mean to have two line segments having the same length?

A

Congruent

Geometry (11 decks)

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