Section 1
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complement theorem
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Last updated
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Date created
Mar 1, 2020
Cards (122)
Section 1
(50 cards)
complement theorem
If angle 1 and 2 form a right angle, then m∠1 + m∠2 = 90
90
supplementary angle of 90
80
supplementary angle of 100
x = 35
Solve for x
angle addition postulate
D is the interior of ∠ABC iff m∠ABD + m∠DBC = m∠ABC
x=5
Solve for x
x = 21
Solve for x
135
supplementary angle of 45
65
complimentary angle of 25
Right angle
B=90
vertical angles theorem
if two angles are verticle, then they are congruent
75
complimentary angle of 15
ray
a part of a line with one end point that extends forever Ex. AB (with one arrowhead direction on top)
opposite rays
2 rays that share the same endpoint but extend in opposite directions. They form a line
Vertical Angles
A pair of opposite congruent angles formed by intersecting lines
30
complimentary angle of 60
43
complimentary angle of 47
complementary angles
two angles with measures that have a sum of 90 degrees and don't have to be next to each other
Adjacent angles
two angles that lie in the same plane and have a common vertex and a common side, but no common interior points, formed by two intersecting lines
70
complimentary angle of 20
Angle
Two rays originating from the same endpoint
Adjacent Angle
Angles that have the same vertex, share a common side, and do not overlap.
x = 8
Solve for x
Linear Pair
Two adjacent angles that form a straight line
Obtuse angle
180> m∠C >90
Linear pair
a pair of adjacent angles with non common sides that are opposite rays (form a straight line), unlike supplementary they cant be separated, they form 180 degrees
linear pair postulate
If angles 1 and 2 form a linear pair, then m∠1 + m∠2 = 180
x = 15
Solve for x
140
supplementary angle of 40
x = 10
Solve for x
Congruent supplements theorem
angles supplementary to the same angle or to congruent angles are congruent. Ex. If angle 1 + angle 2= 180, and angle 2 and angle 3=180 then angle 1 is congruent to angle 3
x = 105
Solve for x
Sides of an angle
The rays of the angle, named just like a ray with commas in between them
3 ways to name an angle
1. Three letters, vertex in the middle, in all caps, Ex. ∠ABC 2. Vertex, if it is the only angle in the diagram. Ex. ∠B 3. Number, if it is given. Ex. ∠2
vertical angles
Two non-adjecent angles formed by two intersecting lines. They are across from one another and MUST be congruent
supplementary angles
two angles that add together to make 180 degree angle or a straight line
x = 29
Solve for x
Acute angle
B<90
Congruent
Having the same size and shape
Vertex
The endpoint or origin of an angle, measured in degrees. Ex. Vertex A
x = 47
Solve for x
x = 17
Solve for x
33
complimentary angle of 57
x = 9
Solve for x
x = 25
Solve for x
160
supplementary angle of 20
vertically opposites
vertical angles that are opposite to each other
Supplementary Angles
Two angles whose sum is 180 degrees (do not have to be adjacent)
83
complimentary angle of 7
complimentary angles
two angles that add together to make a 90 degree angle or a right angle
Section 2
(50 cards)
9 Units
What is the length of side AB with endpoints A(-5, 3) and B(4, 3)?
144⁰
180⁰
5
Find the distance given the following end points. (-2, 1) and (1, 5)
18⁰
Point
An exact position or location on a set of elements (a space, a plane)
parallel lines
a set of lines that is the same distance apart at all points and will never intersect
∠GFA
∠AEC
127⁰
35⁰
∠BED
Definition of angle bisector
A ray, segment, line that divides an angle into two congruent parts
4
Find the distance given the following end points. (-6, -10) and (-2, -10)
Definition of vertical angles
Angle 1 and angle 2 are vertical angles iff they are nonadjacent angles formed by two intersecting lines
∠BAC
7
Find the distance given the following end points. (-4, 2) and (3, 2)
∠BAM
Definition of complementary
Angle 1 and angle 2 are complementary iff m∠1 + m∠2 = 90
will always be a positive answer
Distance Formula
5 units
What is the length of line segment CD with endpoints (-3, 2) and (2, 2) as shown on the coordinate plane?
(5, 1)
Find the midpoint of the following endpoints. (4, -6) and (6, 8)
∠DEA
congruent complements theorem
angles complementary to the same angle or to congruent angles are congruent
Definition of supplementary
Angle 1 and angle 2 are supplementary if and only if m∠1 + m∠2 = 180
20
Find the distance given the following end points. (5, 9) and (-7, -7)
90⁰
∠ABC
∠BCA
32 Square feet
Shelbi is drawing plans for a garden, measured in feet, which is shown on the coordinate plane, What is the area of Shelbi's garden in square feet?
∠CEB
Will give you an ordered pair as an answer
Midpoint Formula
21 square units
What is the area of the rectangle shown on the coordinate plane?
∠HFM
∠GFC
3
Find the distance given the following end points. (-4, -1) and (-4, -4)
<A
(-3, -3)
Find the midpoint of the following endpoints. (-1, -1) and (-5, -5)
perpendicular lines
a set of lines that intersect to form right angles
(2, -2)
Find the midpoint of the following endpoints. (-1, 1) and (5, -5)
70⁰
(5, 6)
Find the midpoint of the following endpoints. (2, 5) and (8, 7)
2
Find the distance given the following end points. (-3, 4) and (-5, 4)
Definition of linear pair
Angle 1 and angle 2 are a linear pair if and only if the are a pair of adjacent angles with noncommon sides that are apposite rays.
10
Find the distance given the following end points. (0, 0) and (6, 8)
135⁰
(-1, 2)
Find the midpoint of the following endpoints. (-4, 2) and (2, 2)
Definition of congruent angles
angles that have the same measure
80⁰
16 square units
What is the area of the rectangle shown on the coordinate plane?
Section 3
(22 cards)