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問題一覧
1
Addition Property of Equality
If a=b then a+c=b+c
2
Subtraction Property of Equality
If a=b then a-c=b-c
3
Multiplication Property of Equality
If a=b then a×c=b×c
4
Division Property of Equality
If a=b and c≠0 then a/c=b/c
5
Reflexive Propety of Equality
a=a
6
Substitution Property of Equality
If a=b then b can replace a in any expression
7
Transitive Property of Equality
If a=b and b=c then a=c
8
Reflexive Property of Congruence
AB≅AB <A≅<A
9
Transitive Property of Congruence
If AB≅CD and CD≅EF then AB≅EF If <A≅<B and <B≅<C then <A≅<C
10
Segment Addition Postulate
If three points A, B, and C are collinear (on the same line) and point B is between A and C, then AB+BC=AC
11
Definition of Midpoint
A point that lies on a segment and bisects the segment. It divides a segment into two congruent segments.
12
The Distributive Property
a(b+c)=ab+ac
13
Symmetric Property for Equality and Congruence
If a=b then b=a If AB≅DC then DC≅AB
14
Angle Addition Postulate
If point B lies in the interior of <AOC, then m<AOB+m<BOC=m<AOC
15
Vertical Angles Theorem
Vertical angles are congruent
16
Linear Pair Angles are Supplementary
If two angles form a linear pair, then the sum of their measures are 180°
17
Definition of Complementary Angles
Two angles whose measures have sum 90°
18
Definition of Supplementary Angles
Two angles whose measures have sum 180°
19
Definition of Angle Bisector
A ray that divides an angle into two congruent coplanar angles. Its endpoint is at the angle vertex.
20
Corresponding Angles Postulate
Corresponding angles are congruent if the transversal intersects two parallel lines.
21
SSIA Theorem
When a transversal intersects two parallel lines, the same side interior angles are supplementary.
22
AIA Theorem
When a transversal intersects two parallel lines, the alternate interior angles are congruent.
23
SSEA Theorem
When a transversal intersects two parallel lines, the same side exterior angles are supplementary.
24
AEA Theorem
When a transversal intersects two parallel lines, the alternate exterior angles are congruent.
25
Triangle Angle Sum is 180 Degrees
The three interior angles of a triangle will always have a sum of 180°
26
All sides are congruent
Equilateral
27
Two sides are congruent
Isoceles
28
No sides are congruent
Scalene
29
All angles are congruent
Equiangular
30
One angle is 90°
Right
31
One angle is over 90° but below 180°
Obtuse
32
One angle is above 0° but below 90°
Acute
33
Distance Formula
d=√((x2-x1)²+(y2-y1)²)
34
Slope formula
m=(y2-y1)/(x2-x1)
35
Which of these are short pythagorean triples?
3, 4, 5, 5, 12, 13, 8, 15, 17, 7, 24, 25, 9, 40, 41, 12, 35, 37, 11, 60, 61
36
Rotation 90 degrees clockwise
(y, -x)
37
Rotation 90 degrees counterclockwise
(-y, x)
38
Rotation 180 degrees
(-x, -y)
39
Reflection on the x-axis
(x, -y)
40
Reflection on the y-axis
(-x, y)
41
Reflection on the line y=x
(y, x)
42
Reflection on the line y=-x
(-y, -x)
43
Intersection of Medians Center of mass (balancing point) Divides the Medians into 2/3 and 1/3 segments
Centroid
44
Intersection of Perpendicular Bisectors Center of a Circle being circumscribed on a triangle Equidistant from each vertex
Circumcenter
45
Intersection of Angle Bisectors Center of a Circle being inscribed in a triangle Equidistant from the sides
Incenter
46
Midpoints of all sides to the opposite vertex (All 3 makes cool 1/3+2/3 stuff happen)
Median
47
Connects midpoint of two sides Parallel to the opposite side and 1/2 of the value of the opposite side
Midsegment
48
The biggest angle is across from the biggest side The smallest angle is across from the smallest side
true
49
The smallest angle is across from the biggest side The biggest angle is across from the smallest side
false
50
In order to be a triangle, the lengths must satisfy...
a+b>c (c=largest side)
51
Find the possible third side a, x, b (x=missing side)
b-a<x<b+a
52
Pythagreon Theorem
If a triangle is right, then a²+b²=c²
53
What is this image?
The Quadratic Formula
54
If c²=a²+b² then...
right triangle
55
If c²<a²+b² then...
acute triangle
56
If c²>a²+b²
obtuse triangle
57
Exterior Angle Theorem
An exterior angle is equal to the sum of the two remote interior angles.
58
Pick all that are correct for isoceles triangles
If a triangle is isoceles, then base angles are congruent , If 2 angles in a triangle are congruent, then the triangle is isoceles , In an isoceles triangle, the altitude is the angle bisector and the median
59
A triangle is equilateral iff it is equiangular, furthermore, the angles are 60 degrees
true
60
What does iff mean in a theorem?
That the theorem and it's converse are true
61
What theorem is this?
Side Splitter Theorem
62
What theorem is this?
Egg Slicer Theorem
63
What theorem is this?
Triangle Angle Bisector Theorem
64
SSS (congruence and similarity)
side side side
65
AA (similarity)
angle angle
66
SAS (congruence and similarity)
side angle side
67
HL (congruence and similarity)
hypotenuse leg
68
ASA (congruence)
angle side angle
69
AAS (congruence)
angle angle side
70
What is true of congruent and similar triangles?
congruent=all sides and angles are equal similar=all sides are similar (have the same ratio) and all angles are equal
71
Select all properties of proportions for a/b=c/d
ad=bc, a/c=b/d, d/b=c/a, b/a=d/c, a+b/b=c+d/d
72
What is the Golden Ratio? (L:W) (A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle).
1.618:1