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MATH 301 > Ch. 12.4 An Introduction to a Formal Approach to Geometry. > Flashcards

Ch. 12.4 An Introduction to a Formal Approach to Geometry. Flashcards

1
Q

What does geometry call an infinite large flat surface?

A

What is a plane?

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2
Q

What are the locations on a plane called?

A

What are points?

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3
Q

What is considered to be straight and extend infinietely in opposite directions?

A

What is a line?

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4
Q

What are points that lie on the same line?

A

What are collinear points?

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5
Q

What are two lines in the plane that do not intersect or are the same called?

A

What are parallel lines?

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6
Q

What are three or more lines that contain the same point called?

A

What are concurrent lines?

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7
Q

The ________ between two points A and B is the nonnegative difference of the real numbers a and b to which A and B __________.

A

The distance between two points A and B is the ___________ difference of the real numbers a and b to which A and B correspond.

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8
Q

The distance from A and B is written __ or BA.

A

The distance from A and B is written AB or __.

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9
Q

The numbers which are lower case letters a and b are called the ________ of a line.

A

The ________ which are lower case letters a and b are called the coordinates of a line.

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10
Q

This symbol, ͍ , a line with two arrows above a coordinate pair pointing opposite ways means it is a _____.

A

What symbol means a pair of coordinates is a line?

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11
Q

This symbol, __ , a plain line above a coordinate means it is a line ______.

A

What symbol above a pair of coordinates means it is a ____ segment?

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12
Q

This symbol, ͢ a line with an arrow pointing right above a coordinate pair means its a ____.

A

This symbol, ͢ a line with one arrow pointing ____ above a coordinate pair means its a Ray.

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13
Q

What is the union of two line segments with a common endpoint or the union of two rays with a common endpoint called?

A

What is an angle?

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14
Q

What is the common endpoint of an angle called?

A

What is a vertex?

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15
Q

What are the line segments that make up an angle called?

A

What are sides?

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16
Q

The symbol ∠ABC is used to denote _____ ABC.

A

Which symbol is used to denote angle ABC?

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17
Q

What type of shape can one pick any two points in the interior of a polygon, connect the and the line segment is always inside?

A

What is a convex polygon?

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18
Q

What type of shape can one pick any two points in the interior of the polygon, which when connected does not lie entirely inside the polygon?

A

What is a Concave polygon?

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19
Q

A portion of a plane that is not the angle or the interior is called the _______.

A

What is the exterior of the angle?

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20
Q

The convex region of a plane is called the _______ region.

A

The _____ region of a plane is called the interior region.

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21
Q

Two angles that share a vertex, have a side in common, but whose interiors do not intersect are called ________ angles.

A

What are Adjacent Angles?

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22
Q

What is the semicircle device used in geometry to measure angles called?

A

What is a protractor?

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23
Q

The measurement of angle BAC is denotes by the following expression, m(∠BAC).

A

The expression m(∠BAC) is read _________.

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24
Q

An angle measuring less than 90° is called a(n) ______ angle.

A

What is an acute angle?

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25
Q

An angle measuring 90° is called a(n) _______ angle.

A

What is a right angle?

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26
Q

An angle measuring more than 90° but less than 180° is called a(n) ________ angle.

A

What is an obtuse angle?

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27
Q

An angle measuring 180° is called a _____ angle.

A

What is a straight angle?

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28
Q

An angle whose measures are greater than 180° is called a(n) _______ angle.

A

What is a reflex angle?

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29
Q

Any two angles that are not adjacent and have the same measure are called _____ angles.

A

What are congruent vertical angles?

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30
Q

Angles having the same measure are called _____ angles.

A

What are congruent angles?

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31
Q

Line segments having the same length are called _________ segments.

A

What are congruent segments?

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32
Q

The symbol of an equal sign with just a tilde above (⩭) means angles or lines are ________.

A

Which symbol means that angles or lines are congruent?

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33
Q

The sum of two angles whose measures equals 180° are called _________angles.

A

What are supplementary angles?

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34
Q

If two lines intersect to form a right angle the lines are called _________ lines.

A

What are perpendicular lines?

35
Q

The symbol with a horizontal line and a vertical line meeting in the middle (⟂) means line a is ________ to line b.

A

Which symbol means line a is perpendicular to line b?

36
Q

The sum of two angles whose measures equals 90° are called ________ angles.

A

What are complimentary angles?

37
Q

If two lines, L and M, are intersected by a third line, T, we call line T a ___________.

A

What is a transversal?

38
Q

When lines L and M are intersected by a transversal and L is Parallel to M (L || M) then angle 1 and 2 are ___________ angles.

A

What is a corresponding angle?

39
Q

When lines L and M are intersected by a transversal and L is Parallel to M (L || M) then the non adjacent angles (2 & 3) formed are ___________-___________ angles.

A

What is an alternate interior angle?

40
Q

The sum of the measures of the three vertex angles in a triangle is ______°.

A

For which shape do the vertex angles sum to 180°?

41
Q

Due to the angle sum in a triangle theory, a triangle can have at most, one _______ angle or at most one ______ angle.

A

Due to the _____-____ in a triangle theory, a triangle can have at most, one right angle or at most one obtuse angle.

42
Q

A triangle that has an angle of 90° is called a(n) ________ triangle.

A

What is a right triangle?

43
Q

A triangle that has an angle measuring more than 90°, but less than 180° is called a(n) _________ triangle.

A

What is an obtuse triangle?

44
Q

A triangle in which all the angles measure less than 90° is called a(n) ________ triangle.

A

What is an acute triangle?

45
Q

What do we call two points on a line, and all the points that lie between them?

A

What is a line segment?

46
Q

What do we call two distinct lines in the same plane that do not intersect?

A

What are parallel lines?

47
Q

What do we call the union of two segments or rays with a common endpoint?

A

What is an angle?

48
Q

What to we call an angle with a measure less than 90 degrees?

A

What is an acute angle?

49
Q

What do we call an angle that measures 90 degrees?

A

What is a right angle?

50
Q

What do we call an angle with a measure greater than 90 and less than 180?

A

What is an obtuse angle?

51
Q

What do we call an angle that measures 180 degrees?

A

What is a straight angle?

52
Q

What do we call an angle that measures more than 180 degrees?

A

What is a reflex angle?

53
Q

What do we call two angles that share a vertex and a side but no interior points?

A

What are adjacent angles?

54
Q

What do we call two nonadjacent angles formed by two intersecting lines?

A

What are vertical angles?

55
Q

What do we call two angles whose measures add to 180 degrees?

A

What are supplementary angles?

56
Q

What do we call two angles whose measures add to 90 degrees?

A

What are complimentary angles?

57
Q

What do we call two lines that intersect to form a right angle?

A

What are Perpendicular lines?

58
Q

What is a triangle with one right angle?

A

What is a right triangle?

59
Q

What is a triangle with three acute angles?

A

What is an acute triangle?

60
Q

What is a triangle with one obtuse angle?

A

What is an obtuse triangle?

61
Q

When two _____ of a triangle are congruent, the ______ opposite those _____ are congruent.

A

When two sides of a triangle are _________, the angles opposite those sides are _________.

62
Q

Since all three sides of an equilateral triangle are congruent, all three angles are congruent, making them each ______ degrees.

A

Since all three sides of an _______ triangle are congruent, all three angles are congruent, making them each 60 degrees .

63
Q

The two types of equilateral triangles that are not possible are the ________ triangle and the ________ triangle?

A

The obtuse and right triangles are two of the triangles that cannot be _____________ triangles.

64
Q

The two parallel sides of a trapezoid are called _______.

A

Which sides of a trapezoid are called bases.

65
Q

Two angles whose common side is a base of trapezoid are called _______ angles.

A

What are the base angles of a trapezoid?

66
Q

There are _____ pairs of base angles in each trapezoid, one for each base.

A

There are two pairs of _______ angles in each trapezoid, one fore each ______.

67
Q

A pair of angles in a quadrilateral that has no sides in common are called _______ angles.

A

What are opposite angles?

68
Q

A quadrilateral has _____ pairs of opposite angles.

A

A quadrilateral has two pairs of ________ angles.

69
Q

A kite has one pair of ________ angles that are congruent.

A

A kite has one pair of opposite angles that are ____________.

70
Q

A parallelogram’s opposite angles are ________.

A

A parallelogram’s ________ angles are congruent.

71
Q

Since a rhombus is a special kind of ____________, it also has _____ pairs of congruent opposite angles.

A

Since a rhombus is a special kind of parallelogram, it also has two pairs of congruent ________ angles.

72
Q

In a rectangle and square all ______ are 90 degrees, which means they are congruent.

A

In a rectangle and square all angles are 90 degrees which means they are ____________.

73
Q

The base angles of any isosceles trapezoid are __________.

A

The ______ angles of any isosceles trapezoid are congruent.

74
Q

Which quadrilaterals have adjacent sides that are congruent? One has one pair of adjacent sides that are congruent and the other two have all pairs congruent.

A

The following quadrilaterals have adjacent sides that are congruent, tell how many congruent pairs each has.
A Kite has ___ pair; a rhombus and a square have _____ pairs.

75
Q

Which quadrilaterals have opposite sides congruent? one has 1 pair of congruent opposite sides; the other four have two pairs.

A

The following quadrilaterals have opposite sides that are congruent, tell how many congruent pairs each has. the Isosceles trapezoid has __ pair of opposite congruent sides; The other four: a parallelogram, rhombus, rectangle and square all have ___ pairs of opposite congruent sides.

76
Q

In which two quadrilaterals are all angles 90 degrees and considered congruent?

A

All the angles in a rectangle and square are 90 degrees and considered __________.

77
Q

In which six quadrilaterals are the opposite sides parallel? Two have one pair of opposite parallel sides; the other four have two pairs of opposite parallel sides.

A

The trapezoid, isosceles trapezoid have _____ pair of opposite parallel sides; the parallelogram, rhombus, rectangle and square have ____ pairs of opposite parallel sides.

78
Q

In which two quadrilaterals are the adjacent sides always perpendicular?

A

In a rectangle and square the adjacent sides are always _____________.

79
Q

In which quadrilaterals are both diagonals congruent?

A

Diagonals are always ________ in isosceles trapezoid, rectangle and square.

80
Q

In which four quadrilaterals do diagonals intersect at the midpoint?

A

A parallelogram, rhombus, rectangle and square all have diagonals that intersect at the _________.

81
Q

In which three quadrilaterals are the diagonals perpendicular?

A

In a kite, rhombus, and square the diagonals are __________.

82
Q

In which five quadrilaterals are the opposite angles congruent? One has one pair and the other four simply have opposite angles congruent.

A

A kite (only 1 pair), parallelogram, rhombus, rectangle and square all have opposite angles that are __________.

83
Q

The _______ trapezoid is the only quadrilateral whose base angles are congruent.

A

The isosceles trapezoid is the only quadrilateral whose _________ angles are congruent.

84
Q

In which quadrilaterals are opposite angles bisected by a diagonal? One has only one pair and the other two have two pair.

A

A kite has one pair of opposite angles _________ by a diagonal and the rhombus and square have two pairs of opposite angles _________ by a diagonal.

MATH 301 (23 decks)

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