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Advanced Geometry Mr. Hamilton > Final Exam > Flashcards

Final Exam Flashcards

1
Q

What is the box or pigeon hole principle?

A

If you have more marbles than boxes and each marble must go in a box, then at least 1 box has multiple marbles.

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2
Q

What is a point?

A

A singular location with no size, is infinitely small, has no dimensions. It is named with capital letters.

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3
Q

What is a line?

A

A “moving point”, it travels in two opposite directions forever. It is one dimensional, named by 2 points, never bends or curves, and is infinitely thin.

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4
Q

What is a plane?

A

A infinitely short/flat/thin surface that spans outward in all directions. It is named with 3 points.

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5
Q

What is a segment or line segment?

A

A “line” that starts out at one point and ends at another. Or a part of a line formed between two points.

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6
Q

What is a ray?

A

A “line” that extends in one direction forever. Or a part of a line that has one endpoint.

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7
Q

What is an angle?

A

2 rays with a common endpoint.

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8
Q

What are collinear points?

A

2 or more points that are on the same line.

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9
Q

What are coplanar points?

A

2 or more points on the same plane.

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10
Q

(Postulate)Two lines intersect to form a….

A

Point.

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11
Q

(Postulate)Two planes intersect to form a……

A

Line.

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12
Q

(Postulate)Through any two points there is exactly one…..

A

Line.

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13
Q

(Postulate)Through any 3 non-collinear points there is exactly one…..

A

Plane.

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14
Q

(Postulate)If you take two points in a plane, then the line containing those points must…..

A

Be on the same plane

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15
Q

What is inductive reasoning?

A

Reaching conclusions based on observations.

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16
Q

What is a sequence?

A

A list of numbers.

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17
Q

What is a term?

A

A number in the list?

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18
Q

What is an arithmetic sequence?

A

A sequence where you add/subtract the same number between consecutive terms.

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19
Q

What is a geometric sequence?

A

A sequence where you multiply by the same number between consecutive terms.

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20
Q

What are congruent segments?

A

2 segments having the same length.

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21
Q

What is a midpoint?

A

A point splitting a segment into 2 congruent segments.

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22
Q

What is the segment addition postulate?(SAP)

A

The distance from A to B and B to C is equal to the distance from A to C. (Part+Part=Whole)

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23
Q

What are complementary angles?

A

2 angles that add up to 90 degrees.

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24
Q

What are supplementary angles?

A

2 angles that add up to 180 degrees.

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25
Q

What are the three types of angles?

A
  1. Acute(below 90)
  2. Right(90)
  3. Obtuse(Above 90)
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26
Q

What are congruent angles?

A

2 angles with equal measures.

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27
Q

What is an angle bisector?

A

A ray that splits an angle into two congruent angles.

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28
Q

What are adjacent angles?

A

Two angles that:

  1. Have the same vertex
  2. Share a ray
  3. Dont overlap
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29
Q

What is a linear pair of angles?

A

2 adjacent angles that form a line.

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30
Q

What is the angle addition postulate?(AAP)

A

AVB+BVC=AVC.(Part+Part=Whole)

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31
Q

What is a median?

A

A line segment involving a triangle going from a vertex to the midpoint of the opposite side.

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32
Q

What is a centroid?

A

The point where the 3 medians of a triangle intersect.

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33
Q

What are the special properties of a centroid?

A
  1. Center of balance/gravity/mass

2. Centroid splits the medians into a 1/3 to 2/3 ratio

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34
Q

What is an altitude?

A

A segment involving a triangle going from a vertex perpendicular to the opposite side.

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35
Q

What is an orthocenter?

A

The point where the three altitudes of a triangle intersect.

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36
Q

What are parallel lines?

A

2 lines on the same plane that never intersect.

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37
Q

What are perpendicular lines?

A

2 lines that intersect to form a right angle.

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38
Q

What is a perpendicular bisector?

A

A line that intersects another line segment at its midpoint.

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39
Q

What is an incenter?

A

Thw point where the 3 angle bisectors of a triangle intersect.

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40
Q

What is an inscribed circle?

A

The circle centered at the incenter of a triangle that fits in the triangle perfectly.

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41
Q

What is the circumcenter?

A

The point where 3 perpendicular bisectors of a triangle intersect.

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42
Q

What is a circumscribed circle?

A

The circle centered at the circumcenter of a triangle that fits outside the triangle perfectly.

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43
Q

What is a conditional statement?

A

A sentence in if(hypothesis,p) then(conclusion) form that can be viewed as true or false.

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44
Q

What is a counterexample?

A

A reason why a statement is false.

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45
Q

What is a converse?

A

If p then q becomes if q then p.

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46
Q

What is the inverse?

A

If p then q becomes if not p then not q.

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47
Q

What is the contrapositive?

A

If p then q becomes if not q then not p.

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48
Q

What property is..

If a=b then a+c=b+c?

A

Addition

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49
Q

What property is….

If a=b then a-c=b-c?

A

Subtraction

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50
Q

What property is….

If a=b then ac=bc

A

Multiplication

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51
Q

What property is….

If a=b then a/c=b/c if c is not equal to zero?

A

Division

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52
Q

What property is

a(b-c)?

A

Distributive

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53
Q

What property is…

a=a?

A

Reflexive

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54
Q

What property is…..

if a=b then b=a

A

Symmetric

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55
Q

What property is…..

If a=b and b=c then a=c?

A

Transative

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56
Q

What property is….

if a=b then a and b can be used interchangably?

A

Substitution

57
Q

What are the three properties of congruence?

A
  1. Reflexive
  2. Symmetric
  3. Transative
58
Q

What is deductive reasoning?

A

Using logic, facts, and general principles to reach an indisputable conclusion.

59
Q

What is a proof?

A

A step by step process using deductive reasoning to show why something must be true.

60
Q

What are acceptable reasons in proofs?

A
  1. Given
  2. Definitions
  3. Properties
  4. Postulates
  5. Previously proven theorems
61
Q

What are vertical angles

A

Pairs of angles formed by intersecting lines that are not adjacent.

62
Q

What is the vertical angles theorem?(VAT)

A

If angles are vertical, they are congruent.

63
Q

What is the overlapping angles theorem?(OST)

A

If AB=CD the AC=CD. If two congruent segments have the same overlapping segment, then the two larger overlapping segments are congruent.

64
Q

What is the overlapping angles theorem?(OAT)

A

If AVB=CVD the AVC=BVD. If two congruent angles share the same overlapping angles, then the two larger overlapping angles are congruent.

65
Q

What is a transversal?

A

A line that intersects two coplanar lines at different points.

66
Q

What are interior angles?

A

Angles formed by a transversal that are “between” the coplanar lines.

67
Q

What are exterior angles?

A

Angles formed by a transversal that are outside the coplanar lines.

68
Q

What are corresponding angles?

A

Pairs of angles formed by a transversal that:

  1. have different vertices
  2. One is interior, one is exterior
  3. On the same side of the transversal
69
Q

What are alternate interior angles?

A

Pairs of angles formed by a transversal that:

  1. Have different vertices
  2. Both are interior angles
  3. Not on the same side of the transversal
70
Q

What are same side interior angles?

A

Pairs of angles formes by a transversal that:

  1. Have different vertices
  2. Are interior angles
  3. Are on the same side of a transversal
71
Q

What are alternate exterior angles?

A

Pairs of angles formed by a transversal that:

  1. Have different vertices
  2. Both are exterior angles
  3. On different sides of the transversal
72
Q

What is the corresponding angles postulate?(CAP)

A

If a transversal cuts two lines that the corresponding angles are congruent, then the lines are parallel.

73
Q

What is the alternate interior angles theorem?(AIAT)

A

If a transversal cuts the two lines so that the alternate interior angles are congruent, then the line is parallel.

74
Q

What is the same-side interior angles theorem?(SSIAT)

A

If a transversal cuts two lines so that the same-side interior angles are supplementary, then the lines are parallel.

75
Q

What is the alternate exterior angles theorem?(AEAT)

A

If a transversal cuts two lines so that the alternate exterior angles are congruent, then the lines are parallel.

76
Q

What is the converse of the angles postulate?(CCAP)

A

If a transversal cuts two parallel lines, then the corresponding angles are congruent.

77
Q

What is the converse of the alternate interior angles theroem?(CAIAT)

A

If a transversal cuts two parallel lines, then the alternate interior angle pairs are congruent.

78
Q

What is the converse of the same-side interior angles theorem?

A

If a tranversal cuts two parallel lines, then the same side interior angle pairs are supplementary.

79
Q

What is the converse of the alternate exterior angles theorem?

A

If a transversal cuts two parallel lines, then the alternate exterior angle pairs are congruent.

80
Q

What are remote interior angles?

A

In a triangle, the interior angles that are not adjacent to adjacent to a given exterior angle.

81
Q

What is the triangle exterior angles theorem?

A

In any triangle, the measure from an exterior angle is equal to the sum of the measures of its remote interior angles.

82
Q

What is the polygon exterior angles theorem?

A

In any polygon, the sum of the measures of a set of exterior angles in 360.

83
Q

What is the parallel postulate?

A

Given any line and a point not on the line, there is a line parallel to the given line through the given point.

84
Q

What is a polygon?

A

A connected set of at least three coplanar line segments such that each segment only intersects two others, one at each midpoint.

85
Q

What is a triangle?

A

A three sided polygon.

86
Q

What are interior angles of polygons?

A

Angles inside a polygon which are formed by two adjacent sides of the polygon.

87
Q

What are exterior angles of polygons?

A

An angle outside a polygon which is formed by extending the side of the polygon.

88
Q

How are the angle of depression and angle of elevation related?

A

They are congruent to each other.

89
Q

What is the definition of similar polygons?

A

Two polygons are similar if one is a dilation of the other.

90
Q

What are the criteria for polygons to be congruent?

A

Two polygons are similar if and only if there is a correspondance such that:

  1. Matching sides have to have the same ratio/scale factor
  2. Matching angles are congruent
91
Q

What is the center of a regular polygon?

A

The center of its circumscribed circle.

92
Q

What is the apothem?

A

A line segment going from the center of a regular polygon perpendicular to a side.

93
Q

What is the definition of a circle?

A

A set of points equidistant from a given centerpoint.

94
Q

What is a tangent line of a circle?

A

A line intersecting the circle exactly one time.

95
Q

What is a point of tangency?

A

The point where a tangent line intersects a circle.

96
Q

What is a radius?

A

A segment going from the center of a circle to a point on the circle.

97
Q

What are congruent circles?

A

2 circles with congruent radii.

98
Q

What are concentric circles?

A

Circles with the same centerpoint.

99
Q

What is a chord?

A

A line segment with both endpoints on the circle.

100
Q

What is diameter?

A

A chord going through the center of a circle.

101
Q

What is a secant line?

A

A line intersecting a circle twice.

102
Q

What is a central angle?

A

An angle whos vertex is at the center of a circle.

103
Q

What is an inscribed angle?

A

An angle inside of a circle whose vertex is on the circle.

104
Q

What is an arc?

A

Part of a circle.

105
Q

What is a major arc?

A

An arc that is more han half of a circle.

106
Q

What is a minor arc?

A

An arc that is less than half of a circle.

107
Q

What is a semicircle?

A

Half of a circle.

108
Q

What is the chord-chord power theorem?

A

If two chords of a circle intersect inside the circle, then the product of the measures of the segments is equal to the product of the measures of the segments of the other chord.

109
Q

What is the secant-secant power theorem?

A

If two secant segments are drawn from a point outside a circle, then the product of the measures of one entire secant segment with its outside oart is equal to the product of the other secant segment with its outside part.

110
Q

What are the pyrhagorean triples?

A

3-4-5
5-12-13
8-15-17
7-24-25

111
Q

What is formed if you draw a radius from the center of a circle to the point of tangency?

A

Two 90 degree angles are formed.

112
Q

Tangent segments to a circle from a point outside the circle are….?

A

Congruent.

113
Q

What is surface area?

A

The combined area of all face or sides of a 3-d figure.

114
Q

What volume and its formula?

A

V=Bh

Volume is how mucn capacity a 3-d object has inside.

115
Q

What is Cavalieri’s principle?

A

Volume doesnt change based of how a figure is “stacked”

Example: Stack of pennies

116
Q

What is the formula for volume of a pyramid or cone?

A

V=1/3•Bh

117
Q

What is the formula for surface area of a cylinder?

A

2•pi•r(squared)+2•pi•r•h

118
Q

What is the formula for volume of a sphere?

A

4/3•pi•r(CUBED)

119
Q

What is the formula for surface area of a sphere?

A

4•pi•r(squared)

120
Q

What is correspondence?

A

A way to pair two points between two polygons.

121
Q

What is the polygon congruence postulate?(PCP)

A

Two polygons are congruent if and only if there is a correspondence between them such that:

  1. All pairs of corresponding sides are congruent
  2. All pairs of corresponding angles are congruent.
122
Q

What is the triangle inequality theorem?

A

For a triangle to be formed, the sum of the legs of the two sides must be greater than the 3rd for all
possible arrangements.

123
Q

What is a parallelogram?

A

A quadrilateral that has two pairs of parallel sides.

124
Q

What is a rectangle?

A

A quadrilateral with four right angles.

125
Q

What is a rhombus?

A

A quadrilateral with four congruent sides.

126
Q

What is a square?

A

A quadrilateral with four right angles and four congruent sides.

127
Q

What is a kite?

A

A quadrilateral with two pairs of congruent, adjacent, sides and its opposite sides are not congruent.

128
Q

What is a transformation?

A

The process of moving a figure in a plain.

129
Q

What is a preimage?

A

An image before it’s moved.

130
Q

What is an image?

A

An image after it’s been moved.

131
Q

What is a rigid transformation?

A

A transformation that preserves the size and shape of a figure.

132
Q

What is an isosceles triangle?

A

A triangle with at least two congruent sides.

133
Q

What is an equilateral triangle?

A

A triangle with three congruent sides.

134
Q

What is an equilateral polygon?

A

A polygon with all sides congruent.

135
Q

What is an equiangular polygon?

A

A polygon with all angles congruent.

136
Q

What is a quadrilateral?

A

A four sided polygon.

137
Q

What js a trapezoid?

A

A quadrilateral with EXACTLY one pair of parallel sides.

138
Q

What does concurrent mean?

A

Multiple lines intersect at the same point.

Advanced Geometry Mr. Hamilton (5 decks)

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