Benchmark Review Flashcards
(68 cards)
1
Q
Point
A
– A point has no dimension . It is a location on a plane. It is represented by a dot.
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.
3
Q
Plane
A
– A plane has two dimensions extending without end. It is often represented by a parallelogram.
4
Q
Line segment
A
– A line segment consists of two endpoints and all the points between them.
5
Q
Ray
A
– A ray has one endpoint and extends without end in one direction.
6
Q
__
BC
(Geometric Notation)
A
Segment BC
7
Q
–>
BC
(Geometric Notation)
A
Ray BC
8
Q
BC
Geometric Notation
A
Line BC
9
Q
BC
Geometric Notation
A
Length of BC
10
Q
∠ABC
Geometric Notation
A
Angle ABC
11
Q
m∠ABC
Geometric Notation
A
Measure of angle ABC
12
Q
△ABC
Geometric Notation
A
Triangle ABC
13
Q
॥
Geometric Notation
A
Is parallel to
14
Q
⟂
Geometric Notation
A
Is perpendicular to
15
Q
≅
A
Is congruent to
16
Q
~
Geometric Notation
A
Is similar to
17
Q
V
Logic Notation
A
Or
18
Q
⋀
A
And
19
Q
➝
A
Read “implies ” , if … then…
20
Q
↔
A
Read “ if and only if ”
21
Q
iff
A
Read “if and only if”
22
Q
～
A
Not
23
Q
∴
A
Therefore
24
Q
Conditional Statement
A
A logical argument consisting of a set of premises.
Hypothesis ( p ) , and Conclusion ( q )
25
Conditional Statement
Symbolically:
If p , then q
p➝q
26
Converse
Formed by interchanging the hypothesis and conclusion of a conditional statement
27
Inverse
Formed by negating the hypothesis and conclusion of a conditional statement
28
Contrapositive
Formed by interchanging and negating the hypothesis and conclusion of a conditional statement
29
Conditional
If p , then q
| p ➝ q
30
Converse
If q , then p
| q ➝ p
31
Inverse
If not p , then not q
| ～p ➝ ～q
32
Contrapoative
If not q , then not p
| ～q ➝ ～p
33
Deductive Reasoning
Method using logic to draw conclusions based upon definitions, postulates, and theorems
34
Inductive Reasoning
Method of drawing conclusions from a limited set of observations
35
Proof
A justification logically valid and based on initial assumptions, definitions, postulates, and theorems
36
Law of Detachment
Deductive reasoning stating that if the hypothesis of a true conditional statement is true then the conclusion is also true
37
Law of Detachment
If p ➝ q is a true conditional statement and p is true, then q is true.
38
Law of Syllogism
Deductive reasoning that draw s a new conclusion from two conditional statements when the conclusion of one is the hypothesis of the other
39
Law of Syllogism
If p ➝ q and q ➝ r are true conditional statements, then p ➝ r is true.
40
Counterexample
Specific case for which a conjecture is false
41
Perpendicular Lines
Two lines that intersect to form a right angle
42
Parallel Lines
Lines that do not intersect and are coplanar
43
Skew Lines
Lines that do not intersect and are not coplanar
44
Transversal
A line that intersects at least two other lines
45
Corresponding Angles
Angles in matching positions when a transversal crosses at least two lines
46
Alternate Interior Angles
Angles inside the lines and on opposite sides of the transversal
47
Alternate Exterior Angles
Angles outside the two lines and on opposite sides of the transversal
48
Consecutive Interior Angles
Angles between the two lines and on the same side of the transversal
49
Midpoint
Divides a segment into two congruent segments
50
Midpoint Formula
Given Points
A ( x 1 , y 1 ) and B ( x 2 , y 2 )
midpoint M = (x1 -x2) (y1 - y2)
--------- ----------
2 2
51
Slope Formula
Ratio of vertical change to horizontal change
slope = m = change in x = y2 - y1
----------------- --------------
change in y x2 - x1
52
Slopes of Lines
Parallel lines have the same slope.
53
Slopes of Lines
Perpendicular lines have slopes whose product is - 1.
54
Slopes of Lines
Vertical lines have undefined slope.
55
Slopes of Lines
Horizontal lines have 0 slope.
56
Distance Formula
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
Perpendicular Bisector
A segment, ray, line, or plane that is perpendicular to a segment at its midpoint
58
Constructions
Traditional constructions involving a compass and straightedge reinforce students’ understanding of geometric concepts.
59
Scalene
| Classifying Triangles
No congruent sides
| No congruent angles
60
Isosceles
| Classifying Triangles
At least 2 congruent sides
| 2 or 3 congruent angles
61
Equilateral
| Classifying Triangles
3 congruent angles
| All equilateral triangles are isosceles
62
Acute
| Classifying Triangles
3 acute angles
| 3 angles, each less than 90°
63
Right
| Classifying Triangles
1 right angle
| 1 angle equals 90°
64
Obtuse
| Classifying Triangles
1 obtuse angle
| 1 angle greater than 90°
65
Equiangular
| Classifying Triangles
3 congruent angles
| 3 angles, each measures 60°
66
Triangle Sum Theorem
Measures of the interior angles of a triangle = 180°
| m∠A + m∠B + m∠C = 180°
67
Exterior Angle Theorem
Exterior angle, m∠ 1, is equal to the sum of the measures of the two non adjacent interior angles.
68
Pythagorean Theorem
If △ABC is a right triangle, then a 2 + b 2 = c 2 .
