Study sets matching "geometry theorems"
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ReflexiveProperty
SymmetricProperty
TransitiveProperty
Add/Subtract Property
For every number a, a = a.
For all numbers a & b, if a = b, then b = a.(ex. the segment G…
For all numbers a, b & c, if a = b & b = c, then a = c. (A bit…
For all numbers a, b, & c, if a = b, then a + c = b + c and a…
ReflexiveProperty
For every number a, a = a.
SymmetricProperty
For all numbers a & b, if a = b, then b = a.(ex. the segment G…
congruent complement theorem
congruent complement theorem example
congruent supplements theorem
congruent supplements theorem example
2 angles that are complementary to the same angle and have to…
angle 1=25, angle 2=65 If I know angle 3 is complementary to a…
2 angles that are supplementary to the same angle and have to…
angle 1=100, angle 2=80 If I know angle 3 is supplementary to…
congruent complement theorem
2 angles that are complementary to the same angle and have to…
congruent complement theorem example
angle 1=25, angle 2=65 If I know angle 3 is complementary to a…
Right angle congruence theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Linear pair postulate
All right angles are congruent.
If two angles are supplementary to the same angle, or to congr…
If two angles are complementary to the same angle, or to congr…
If two angles form a linear pair, then they are supplementary.
Right angle congruence theorem
All right angles are congruent.
Congruent Supplements Theorem
If two angles are supplementary to the same angle, or to congr…
theorem 1
theorem 2
theorem 3
postulate
if a quadrilateral has 2 sets of opposite sides congruent, the…
congruence of segments is reflexive, symmetric, and transitive…
perpendicular lines intersect to form 4 right angles if 2 angl…
if 2 parallel lines are cut by a transversal, then the corresp…
theorem 1
if a quadrilateral has 2 sets of opposite sides congruent, the…
theorem 2
congruence of segments is reflexive, symmetric, and transitive…
3.1
3.2 Alternate Interior Angles (AIA) The…
3.3 Consecutive Interior Angles (CIA) T…
Alternate Exterior Angles (AEA) Theorem
If two parallel planes are cut by a third plane, then the line…
If two parallel lines are cut by a transversal, then alternate…
If two parallel lines are cut by a transversal, then the same-…
If two parallel lines are cut by a transversal, then alternate…
3.1
If two parallel planes are cut by a third plane, then the line…
3.2 Alternate Interior Angles (AIA) The…
If two parallel lines are cut by a transversal, then alternate…
Theorem 1
Theorem 1a
Theorem 2
Theorem 2a
If 2 angles are equal then their supplements are equal
If 2 supplements are equal then the angles are equal
If 2 angles are equal then their complements are equal
If 2 complements are equal them the angles are equal
Theorem 1
If 2 angles are equal then their supplements are equal
Theorem 1a
If 2 supplements are equal then the angles are equal
linear pair theorem
congruent supplements theorem
right angle congruence theorem
congruent complements theorem
if two angles form a linear pair, then they are supplementary
if two angles are supplementary to the same angle (or two cong…
all right angles are congruent
if two angles are complementary to the same angle ( or two con…
linear pair theorem
if two angles form a linear pair, then they are supplementary
congruent supplements theorem
if two angles are supplementary to the same angle (or two cong…
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Theorem 2-4
Vertical angles are congruent
If 2 angles are supplements of the same angle (or congruent an…
If 2 angles are complements of the same angle (of congruent an…
All right angles are congruent.
Vertical Angles Theorem
Vertical angles are congruent
Congruent Supplements Theorem
If 2 angles are supplements of the same angle (or congruent an…
Theorem
Vertical Angles Theorem (2-1)
Congruent Supplements Theorem (2-2)
Congruent Complements Theorem (2-3)
a statement that you prove or that is proven to be true
vertical angles are congruent
if 2 angles are supplements of the same angle or of congruent…
if 2 angles are complements of the same angle or of congruent…
Theorem
a statement that you prove or that is proven to be true
Vertical Angles Theorem (2-1)
vertical angles are congruent
Congruent complements theorem
Congruent supplements theorem
Right angle congruency theorem
Linear pair postulate THENTHE
If two angles are complementary to the same angle then the ang…
If two angles are supplementary to the same angle then they ar…
All right angles are 90 degrees
If two angles form a linear pair then they are 180 degrees
Congruent complements theorem
If two angles are complementary to the same angle then the ang…
Congruent supplements theorem
If two angles are supplementary to the same angle then they ar…
Congruences of segments
Congruence of angles
Right angles congruence theorem
Congruent supplements theorem
Segement congruence is reflexive, symmetric, transitive
Angle congruence is reflexive, symmetric, transitive
All right angles are congruent
If two angles are supplementary to the same angle, then they a…
Congruences of segments
Segement congruence is reflexive, symmetric, transitive
Congruence of angles
Angle congruence is reflexive, symmetric, transitive
Triangle Midsegment Theorem
Perpendicular Bisector Theorem
Converse of Perpendicular Bisector Theo…
Angle Bisector Theorem
If a segment joins the midpoints of two sides of a triangle, t…
If a point is on the perpendicular bisector of a segment, then…
If a point is equidistant from the endpoints of a segment, the…
If a point is on the bisector of an angle, then the point is e…
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, t…
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then…
Therom 1.1
Theorem 1.2
Theorem 1.3
Theorem 2.1
Congruence of segments is reflexive, symetric, and transitive.
If two segments are congruent to the same segment, then they a…
If two angles are congruent to the same angle, then they are c…
The sum of the measures of the angles in a linear pair is 180.
Therom 1.1
Congruence of segments is reflexive, symetric, and transitive.
Theorem 1.2
If two segments are congruent to the same segment, then they a…
Adjacent angles sum theorem
Linear pair theorem
Vertical angle theorem
Midpoint theorem
If each of two adjacent angles is congruent to another angle i…
Angles that form a linear pair are supplementary
Vertical angles are congruent
If M is the midpoint of segment A.B. then AM equals one half AB
Adjacent angles sum theorem
If each of two adjacent angles is congruent to another angle i…
Linear pair theorem
Angles that form a linear pair are supplementary
Theorem
Linear Pair Postulate
Segment Addition Postulate
Angle Addition Postulate
a statement that can be proven
if two angles form a linear pair, then the angles are suppleme…
If point B is on AC and between points A and C, then AB+BC=AC
If point D lies on the interior of <ABC, then m<ABD+m<DBC=m<ABC
Theorem
a statement that can be proven
Linear Pair Postulate
if two angles form a linear pair, then the angles are suppleme…
Vertical Angles Theorem
Congruent Supplements Theorem
Right Angle Congruence Theorem
Right Angle Supplements Theorem
If two angles are vertical angles, then they are congruent.
If two angles are supplementary to the same angle (or to congr…
All right angles are congruent
If two angles are congruent and supplementary, then each is a…
Vertical Angles Theorem
If two angles are vertical angles, then they are congruent.
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congr…
Chapter 2
Vertical Angles Theorem 2-1
Congruent Supplements 2-2
Congruent Complements 2-3
...
vertical Angles are congruent
If two angles are supplements of the same angle (or of congrue…
If two angles are complements of the same angle ( or of congru…
Chapter 2
...
Vertical Angles Theorem 2-1
vertical Angles are congruent
If two angles are right angles, then...
If two angles are straight angles, then…
If a condition statement is true, then.…
If angles are supplementary to the same…
they are congruent
they are congruent
the contrapositive of the statement is true
they are congruent
If two angles are right angles, then...
they are congruent
If two angles are straight angles, then…
they are congruent
Protractor Postulate
Angle Addition Postulate
Theorem #3
Theorem #4
guarantees that rays can be paired with the numbers between 0…
allows angle measure to be added; ex: if D is the interior of…
If two angles form a linear pair, then they are supplementary
If the noncommon sides of two adjacent angles form a right ang…
Protractor Postulate
guarantees that rays can be paired with the numbers between 0…
Angle Addition Postulate
allows angle measure to be added; ex: if D is the interior of…
If two parallel lines are cut by a tran…
If two parallel lines are cut by a tran…
If two parallel lines are cut by a tran…
If two parallel lines are cut by a tran…
then alternate interior angles are congruent
then alternate interior angles are congruent
then alternate exterior angles are congruent
the interior angles on the same side of the transversal are su…
If two parallel lines are cut by a tran…
then alternate interior angles are congruent
If two parallel lines are cut by a tran…
then alternate interior angles are congruent