Download List of Reasons Version 4.0 1. Given 2. Addition 3. Subtraction 4

List of Reasons Version 4.0
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Given
Addition
Subtraction
Multiplication
Division
Eq. Prop. of Addition
Eq. Prop. of Subtraction
Eq. Prop. of Division
Eq. Prop. of Multiplication
Substitution
Distributive Prop.
Reflexive Prop.
Symmetric Prop.
Transitive Prop.
Additive Id.
Multiplicative Id.
Zero Product Prop.
Commutative Prop. of Addition
Commutative Prop. of Multiplication
Associative Prop. of Addition
Associative Prop. of Multiplication
Additive Inverse
Multiplicative Inverse
Divisive Prop. of One
Segment Addition Postulate
Def. of Midpoint (a point that divides a segment into 2 equal parts)
Def. of Segment Bisector (a line or segment that divides a different segment into 2
equal parts.)
Angle Addition Postulate
Def. of Angle Bisector (a line or ray that divides an angle into two equal parts.)
Def. of Acute Angle (angle measuring between 0 and 90 degrees.)
Def. of Right Angle (angle measuring exactly 90 degrees.)
Def. of Obtuse Angle (angle measuring between 90 and 180 degrees.)
Def. of Straight Angle (angle measuring exactly 180 degrees or angle formed by
opposite rays.)
Vertical Angles are Congruent
Def. of Complementary Angles (two or more angles whose sum is 90 degrees.)
Def. of Supplementary Angles (two or more angles whose sum is 180 degrees.)
Def. of Linear Pair (two adjacent angles whose non-common sides form opposite
rays.)
Linear Pairs are Supplementary
Def of Perpendicular Lines (intersecting lines that form right angles or intersecting
lines that form right angles are perpendicular.)
If two lines are parallel, then corresponding angles are congruent.
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If two lines are parallel, then alternate interior angles are congruent.
If two lines are parallel, then alternate exterior angles are congruent.
If two lines are parallel, then consecutive interior angles are supplementary.
In a plane, if a line is perpendicular to one of two parallel lines, then it is
perpendicular to the other.
In a plane, if a line is parallel to one of two parallel lines, then it is parallel to the
other.
If corresponding angles are congruent, then lines are parallel.
If alternate interior angles are congruent, then lines are parallel.
If alternate exterior angles are congruent, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
In a plane, two lines perpendicular to the same line are parallel.
All right angles are congruent.
Def. of Acute Triangle (all three angles are acute)
Def. of Right Triangle (one angle is a right angle)
Def. of Obtuse Triangle (one angle is an obtuse angle)
Def. of Equiangular Triangle (all angles are congruent)
Def. of Isosceles Triangle (at least two sides are congruent)
Def. of Scalene Triangle (no sides are congruent or all sides are different)
Def. of Equilateral Triangle (all sides are congruent)
The sum of the measures of the interior angles of a triangle equals 180 degrees.
Exterior angles of a triangle equal the sum of the two remote interior angles.
If two angles of a triangle are congruent to two angles of another triangle, then the
third angles are also congruent.
If a triangle is equilateral, then it is also equiangular.
If a triangle is equiangular, then it is also equilateral.
Each angle of an equilateral triangle is 60 degrees.
The acute angles of a right triangle are complementary.
The exterior angle of a triangle is greater than either remote interior angle.
If two sides of a triangle are congruent, then the opposite angles are also congruent.
If two angles of a triangle are congruent, then the opposite sides are also congruent.
Base angles of an Isosceles Triangle are congruent.
SSS
SAS ASA AAS (all separate reasons)
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Def. of Median of a Triangle
Def. of Altitude of a Triangle
Def. of Midsegment of a Triangle
Def. of Centroid
Def. of Orthocenter
Def. of Incenter
Def. of Circumcenter
If two angles of a triangle are congruent, then the triangle is isosceles.
Congruent supplementary angles are right angles.
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Def. of a Kite
Def. of a Parallelogram
Def. of a Rhombus
Def. of a Rectangle
Def. of a Square
Def. of a Trapezoid
Def. of Isosceles Trapezoid
Def. of a Midsegment of a Triangle
Def. of Midsegment of a Trapezoid
The sum of the measures of the n interior angles of an n-gon is 180(n-2) degrees.
The sum of the measures of the set of exterior angles (one at each vertex) of any
polygon is 360 degrees.
92. The nonvertex angles of a kite are congruent.
93. The diagonals of a kite are perpendicular.
94. The diagonal connecting the vertex angles of a kite is the perpendicular bisector of
the other diagonal (the diagonal connecting the nonvertex angles.)
95. The vertex angles of a kite are bisected by a diagonal.
96. The consecutive angles between the bases of a trapezoid are supplementary.
97. The base angles of an isosceles trapezoid are congruent.
98. The diagonals of an isosceles trapezoid are congruent.
99. The three midsegments of a triangle divide it into four congruent triangles.
100. A midsegment of a triangle is parallel to the third side and half the length of the third
side.
101. The midsegment of a trapezoid is parallel to the bases and is equal in length to the
average of the lengths of the bases.
102. The opposite angles of a parallelogram are congruent
103. The consecutive angles of a parallelogram are supplementary.
104. The opposite sides of a parallelogram are congruent.
105. The diagonals of a parallelogram bisect each other.
106. If two parallel lines are intersected by a second pair of parallel lines that are the same
distance apart as the first pair, then the parallelogram formed is a rhombus.
107. The diagonals of a rhombus are perpendicular, and they bisect each other.
108. The diagonals of a rhombus bisect the angles of the rhombus.
109. The diagonals of a rectangle are congruent and bisect each other.
110. The diagonals of a square are congruent, perpendicular, bisect each other and bisect
the angles of a square.