Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Geometry > Benchmark Review > Flashcards

Benchmark Review Flashcards

1
Q

Point

A

– A point has no dimension . It is a location on a plane. It is represented by a dot.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Line

A
  • A line has one dimension. Its is an infinite set of points represented by a line with two arrowheads that extends without end.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Plane

A

– A plane has two dimensions extending without end. It is often represented by a parallelogram.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Line segment

A

– A line segment consists of two endpoints and all the points between them.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Ray

A

– A ray has one endpoint and extends without end in one direction.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

__
BC
(Geometric Notation)

A

Segment BC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

–>
BC
(Geometric Notation)

A

Ray BC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

BC

Geometric Notation

A

Line BC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

BC

Geometric Notation

A

Length of BC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

∠ABC

Geometric Notation

A

Angle ABC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

m∠ABC

Geometric Notation

A

Measure of angle ABC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

△ABC

Geometric Notation

A

Triangle ABC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

॥

Geometric Notation

A

Is parallel to

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

⟂

Geometric Notation

A

Is perpendicular to

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

≅

A

Is congruent to

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

~

Geometric Notation

A

Is similar to

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

V

Logic Notation

A

Or

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

⋀

A

And

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

➝

A

Read “implies ” , if … then…

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

↔

A

Read “ if and only if ”

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

iff

A

Read “if and only if”

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

～

A

Not

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

∴

A

Therefore

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Conditional Statement

A

A logical argument consisting of a set of premises.

Hypothesis ( p ) , and Conclusion ( q )

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Conditional Statement

A

Symbolically:
If p , then q
p➝q

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Converse

A

Formed by interchanging the hypothesis and conclusion of a conditional statement

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Inverse

A

Formed by negating the hypothesis and conclusion of a conditional statement

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Contrapositive

A

Formed by interchanging and negating the hypothesis and conclusion of a conditional statement

29
Q

Conditional

A

If p , then q

p ➝ q

30
Q

Converse

A

If q , then p

q ➝ p

31
Q

Inverse

A

If not p , then not q

～p ➝ ～q

32
Q

Contrapoative

A

If not q , then not p

～q ➝ ～p

33
Q

Deductive Reasoning

A

Method using logic to draw conclusions based upon definitions, postulates, and theorems

34
Q

Inductive Reasoning

A

Method of drawing conclusions from a limited set of observations

35
Q

Proof

A

A justification logically valid and based on initial assumptions, definitions, postulates, and theorems

36
Q

Law of Detachment

A

Deductive reasoning stating that if the hypothesis of a true conditional statement is true then the conclusion is also true

37
Q

Law of Detachment

A

If p ➝ q is a true conditional statement and p is true, then q is true.

38
Q

Law of Syllogism

A

Deductive reasoning that draw s a new conclusion from two conditional statements when the conclusion of one is the hypothesis of the other

39
Q

Law of Syllogism

A

If p ➝ q and q ➝ r are true conditional statements, then p ➝ r is true.

40
Q

Counterexample

A

Specific case for which a conjecture is false

41
Q

Perpendicular Lines

A

Two lines that intersect to form a right angle

42
Q

Parallel Lines

A

Lines that do not intersect and are coplanar

43
Q

Skew Lines

A

Lines that do not intersect and are not coplanar

44
Q

Transversal

A

A line that intersects at least two other lines

45
Q

Corresponding Angles

A

Angles in matching positions when a transversal crosses at least two lines

46
Q

Alternate Interior Angles

A

Angles inside the lines and on opposite sides of the transversal

47
Q

Alternate Exterior Angles

A

Angles outside the two lines and on opposite sides of the transversal

48
Q

Consecutive Interior Angles

A

Angles between the two lines and on the same side of the transversal

49
Q

Midpoint

A

Divides a segment into two congruent segments

50
Q

Midpoint Formula

A

Given Points
A ( x 1 , y 1 ) and B ( x 2 , y 2 )

midpoint M = (x1 -x2) (y1 - y2)
——— ———-
2 2

51
Q

Slope Formula

A

Ratio of vertical change to horizontal change

slope = m = change in x = y2 - y1
—————– ————–
change in y x2 - x1

52
Q

Slopes of Lines

A

Parallel lines have the same slope.

53
Q

Slopes of Lines

A

Perpendicular lines have slopes whose product is - 1.

54
Q

Slopes of Lines

A

Vertical lines have undefined slope.

55
Q

Slopes of Lines

A

Horizontal lines have 0 slope.

56
Q

Distance Formula

A

Given points A ( x 1 , y 1 ) and B ( x 2 , y 2 )

AB = √ (x2 - x1) 2 + (y2 - y1) 2

The distance formula is based on the Pythagorean Theorem.

57
Q

Perpendicular Bisector

A

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint

58
Q

Constructions

A

Traditional constructions involving a compass and straightedge reinforce students’ understanding of geometric concepts.

59
Q

Scalene

Classifying Triangles

A

No congruent sides

No congruent angles

60
Q

Isosceles

Classifying Triangles

A

At least 2 congruent sides

2 or 3 congruent angles

61
Q

Equilateral

Classifying Triangles

A

3 congruent angles

All equilateral triangles are isosceles

62
Q

Acute

Classifying Triangles

A

3 acute angles

3 angles, each less than 90°

63
Q

Right

Classifying Triangles

A

1 right angle

1 angle equals 90°

64
Q

Obtuse

Classifying Triangles

A

1 obtuse angle

1 angle greater than 90°

65
Q

Equiangular

Classifying Triangles

A

3 congruent angles

3 angles, each measures 60°

66
Q

Triangle Sum Theorem

A

Measures of the interior angles of a triangle = 180°

m∠A + m∠B + m∠C = 180°

67
Q

Exterior Angle Theorem

A

Exterior angle, m∠ 1, is equal to the sum of the measures of the two non adjacent interior angles.

68
Q

Pythagorean Theorem

A

If △ABC is a right triangle, then a 2 + b 2 = c 2 .

Geometry (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions