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Study sets matching "geometry theorems"

5 terms
Theorems for geometry.
Right angle Thm( RAT).
Congruent supplements theorem (cst)
Linear pair postulate( llp)
Vertical angle theorem( VAT)
All right angles are congruent. Write they are right angles i…
If two angles are supplementary to the same angle( or to cong…
If 2 angles form a linear pair then they are supplementary.
Vertical angles are congruent.
Right angle Thm( RAT).
All right angles are congruent. Write they are right angles i…
Congruent supplements theorem (cst)
If two angles are supplementary to the same angle( or to cong…
41 terms
Theorems for Geometry
Thm 1.1
Thm 1.2
Thm 1.3
Thm 2.1
Two lines intersect at exactly one point
Through a line and a point not on the line, there is exactly…
If two lines intersect, then exactly one plane contains those…
Midpoint theorem
Thm 1.1
Two lines intersect at exactly one point
Thm 1.2
Through a line and a point not on the line, there is exactly…
45 terms
Geometry Proofs and Theorems
Segment Addition Postulate
Same Side Interior Angle Theorem
Isosceles Triangle Theorem
No Choice Theorem / 3rd Angles Theorem
If three points A, B, and C are collinear and B is between A…
If two lines are cut by a transversal, the same side interior…
If two sides of a ∆ are congruent, then the angles opposite t…
If two angles of a ∆ are congruent to two angles of another ∆…
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A…
Same Side Interior Angle Theorem
If two lines are cut by a transversal, the same side interior…
45 terms
Geometry Proofs and Theorems
Segment Addition Postulate
Same Side Interior Angle Theorem
Isosceles Triangle Theorem
No Choice Theorem / 3rd Angles Theorem
If three points A, B, and C are collinear and B is between A…
If two lines are cut by a transversal, the same side interior…
If two sides of a ∆ are congruent, then the angles opposite t…
If two angles of a ∆ are congruent to two angles of another ∆…
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A…
Same Side Interior Angle Theorem
If two lines are cut by a transversal, the same side interior…
25 terms
Geometry Theorems
vertical angles theorem
if two angles are supplements of the s…
if two angles are complements of the s…
all right angles are __________
vertical angles are congruent
congruent
congruent
congruent
vertical angles theorem
vertical angles are congruent
if two angles are supplements of the s…
congruent
Geometry theorems
1-1 Segment Addition Posulate
1-2 Definition:... ≅ seg
1-2 Definition:... Midpoint of a segment
1-3 Angle Addition Postulate
If point B is between G and S, then GB+BS=GS... If GB+BS=GS, the…
If 2 seg are ≅, then they have = length ... If 2 seg have the =…
If a pt is the MP of a segment, then it ÷s the segment into 2…
If point H is inside ∠GBS, then m∠GBH+m∠SBH=m∠GBS
1-1 Segment Addition Posulate
If point B is between G and S, then GB+BS=GS... If GB+BS=GS, the…
1-2 Definition:... ≅ seg
If 2 seg are ≅, then they have = length ... If 2 seg have the =…
86 terms
Geometry Formulas, Theorems and Vocabulary
The "Undefined Terms of Geometry"...
point
line
plane
point, line, plane
a location in space represented by a dot and usually assigned…
a straight path that extends without end in opposite directions
a flat surface that extends forever
The "Undefined Terms of Geometry"...
point, line, plane
point
a location in space represented by a dot and usually assigned…
39 terms
Geometry Theorems, Postulates, & Definitions
Segment Addition Postulate
Angle Addition Postulate
Definition of Midpoint & Bisector
Definition of Angle Bisector
If B is between A and C then the length of AC is equal to the…
If P is in the interior of ∠RST then the measure of ∠RST is t…
A bisector bisects a line segment at its midpoint which divid…
A ray that divides an angle into two adjacent angles that are…
Segment Addition Postulate
If B is between A and C then the length of AC is equal to the…
Angle Addition Postulate
If P is in the interior of ∠RST then the measure of ∠RST is t…
16 terms
Important Geometry Theorems/Postulates
If two congruent angles form a linear…
If two angles are vertical angles, the…
If there is a line and a point not on…
If there exists a line and a point, th…
If two congruent angles form a linear…
If two angles are vertical angles, the…
65 terms
Geometry Theorems
Linear Pair Theorem
Vertical Angles Theorem
Corresponding Angles Theorem
Alt. Interior Angles Theorem
If two angles form a linear pair then add up to 180 degrees
If two angles are vertical then they are congruent
If 2 parallel lines cut by a transversal form 2 corresponding…
If 2 parallel lines cut by a transversal form 2 alt. interior…
Linear Pair Theorem
If two angles form a linear pair then add up to 180 degrees
Vertical Angles Theorem
If two angles are vertical then they are congruent
14 terms
Theorems in Geometry
Right Angle Congruence Theorem
Congruent Supplement Theorem
Congruent Complements Theorem
Vertical Angles Congruence Theorem
all right angles are congruent... Given:∠1 +∠2 are right angles…
If two angles are supplementary to the same angle (or to cong…
IF two angles are complementary to the same angle (or to cong…
Vertical angles are congruent... Given: ∠1 and ∠2 are vertical ∠…
Right Angle Congruence Theorem
all right angles are congruent... Given:∠1 +∠2 are right angles…
Congruent Supplement Theorem
If two angles are supplementary to the same angle (or to cong…
18 terms
Geometry Theorems
2.1 Properties of Segment Congruence
2.2 Properties of Angles Congruence
2.3 Right Angles Congruence Theorem
2.4 Congruent Supplements Theorem
...
...
...
...
2.1 Properties of Segment Congruence
...
2.2 Properties of Angles Congruence
...
86 terms
Geometry Formulas, Theorems and Vocabulary
The "Undefined Terms of Geometry"...
point
line
plane
point, line, plane
a location in space represented by a dot and usually assigned…
a straight path that extends without end in opposite directions
a flat surface that extends forever
The "Undefined Terms of Geometry"...
point, line, plane
point
a location in space represented by a dot and usually assigned…
86 terms
Geometry Formulas, Theorems and Vocabulary
The "Undefined Terms of Geometry"...
point
line
plane
point, line, plane
a location in space represented by a dot and usually assigned…
a straight path that extends without end in opposite directions
a flat surface that extends forever
The "Undefined Terms of Geometry"...
point, line, plane
point
a location in space represented by a dot and usually assigned…
12 terms
Geometry - Postulates and theorems
segment addition postulate
reflexive property
congruent
midpoint theorem
AB + BC = AC
any segment or angle is congruent/equal to itself (AB = AB) (…
have equal measure
If AB + BC = AC and AB=BC
segment addition postulate
AB + BC = AC
reflexive property
any segment or angle is congruent/equal to itself (AB = AB) (…
71 terms
Geometry Pre AP Theorems
if two lines intersect, then they inte…
through a line and a point not in the…
if two lines intersect, then exactly o…
if M is the midpoint of line AB, then…
point
plane
plane
Midpoint Theorem
if two lines intersect, then they inte…
point
through a line and a point not in the…
plane
8 terms
Geometry Theorems
Theorem 2-1:Midpoint Theorem
Theorem 2-2:Angle Bisector Theorem
Theorem 2-3:
Theorem 2-4
If M is the midpoint of line AB, then = 1/2AB and MB = 1/2AB
If ray BX is the bisector of angle ABC, then the measure of a…
...
...
Theorem 2-1:Midpoint Theorem
If M is the midpoint of line AB, then = 1/2AB and MB = 1/2AB
Theorem 2-2:Angle Bisector Theorem
If ray BX is the bisector of angle ABC, then the measure of a…
10 terms
Geometry Theorems
Theorem #1
Theorem #2
Theorem #3
Theorem #4
If two adjacent angles form a right angle, then they are comp…
If two adjacent angles form a straight angle, then they are s…
If two angles are congruent, then their complements are congr…
If two angles are congruent, then their supplements are congr…
Theorem #1
If two adjacent angles form a right angle, then they are comp…
Theorem #2
If two adjacent angles form a straight angle, then they are s…
8 terms
Geometry Theorems
Theorem 24
Theorem 25
Theorem 26
Theorem 27:
If two points are each equidistant from the endpts of a seg,…
If a point is on the perpendicular bisector of a segment then…
If two nonvertical lines are parallel, then their slopes are…
If the slopes of two nonvertical lines are equal, then the li…
Theorem 24
If two points are each equidistant from the endpts of a seg,…
Theorem 25
If a point is on the perpendicular bisector of a segment then…
16 terms
Geometry Theorems
Theorem 1
Theorem 2
Theorem 4 (SSAC)
Theorem 5 (SCAC)
If two angles are right angles, then they are congruent
If two angles are straight angles, then they are congruent
If angles are supplementary to the same angle, then they are…
If angles are supplementary to congruent angles, then they ar…
Theorem 1
If two angles are right angles, then they are congruent
Theorem 2
If two angles are straight angles, then they are congruent
8 terms
Geometry theorems
Theorem 1- the betweenness of points t…
Theorem 2- the betweenness of rays the…
Theorem 3
Theorem 4
If A-B-C, then AB + BC = AC
If OA-OB-OC, then <AOB + <BOC = <AOC
Complements of the same angle are equal
Supplements of the same angle are equal
Theorem 1- the betweenness of points t…
If A-B-C, then AB + BC = AC
Theorem 2- the betweenness of rays the…
If OA-OB-OC, then <AOB + <BOC = <AOC
5 terms
Geometry Theorems
ASA
AAS
SAS
SSS
Two angles and included side
Two angles and non-included side
Two sides and included angle
Three sides
ASA
Two angles and included side
AAS
Two angles and non-included side
12 terms
Geometry Theorems
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Right Angle Theorem
Vertical angles are congruent
If two angles are supplements of the same or congruent angle…
If two angles are compliments of the same or congruent angle…
All right angles are congruent
Vertical Angles Theorem
Vertical angles are congruent
Congruent Supplements Theorem
If two angles are supplements of the same or congruent angle…
Geometry theorems
Angle Add postulate
Supplement theorem
Complement theorem
Reflexive property of congruence
D is the interior of <ABC if and only if m<abc+m<dbc=ABC
If two angles form a linear pair then they are supplementary
If two no common sides of two adjacent angles form a right an…
Any angle is congruent to its self
Angle Add postulate
D is the interior of <ABC if and only if m<abc+m<dbc=ABC
Supplement theorem
If two angles form a linear pair then they are supplementary
15 terms
Geometry theorems
SSS
SAS
ASA
AAS
if the sides of one triangle are congruent to the sides of a…
if two sides and the included angle of one triangle are congr…
if two angles and the included side of one triangle are congr…
if two angles and a non included side of one triangle are con…
SSS
if the sides of one triangle are congruent to the sides of a…
SAS
if two sides and the included angle of one triangle are congr…
11 terms
geometry theorems
vertical angles theorem
congruent supplements theorem
congruent complements theorem
right angles theorem
if two angles are vertical then they are congruent
if two angles are supplements of the same angle then the two…
if two angles are complements of the same angle then the two…
if two angles are right then they are congruent
vertical angles theorem
if two angles are vertical then they are congruent
congruent supplements theorem
if two angles are supplements of the same angle then the two…
33 terms
Geometry Theorems
Congruent radii theorem
Congruent right angles theorem
Diameter midpoint theorem
Noncommon perpendicular ray complement…
If two line segments are the radii of the same Circle, then t…
If two angles are right angles, then they are congruent
The center of the circle is the midpoint of its diameter
If angles are adjacent with noncommon perpendicular rays, the…
Congruent radii theorem
If two line segments are the radii of the same Circle, then t…
Congruent right angles theorem
If two angles are right angles, then they are congruent
11 terms
Geometry Theorems
Same-side interior angle postulate
Alternate interior angles theorem
corresponding angles theorem
alternate exterior angles theorem
if a transversal intersects two parallel lines then same-side…
if a transversal intersects two parallel lines then alternate…
if a transversal intersects two parallel lines then correspon…
if a transversal intersects two parallel lines then alternate…
Same-side interior angle postulate
if a transversal intersects two parallel lines then same-side…
Alternate interior angles theorem
if a transversal intersects two parallel lines then alternate…
10 terms
Geometry Theorems
Reflexive Property
Midpoint Theorem
Vertical Angle Theorem
Alternate Interior Angle Theorem
For every real number, the number equals itself. Ex. x=x
If M is the midpoint of line AB, then line AM is congruent to…
If two angles are vertical angles, then they are congruent.
If two parallel lines are cut by a transversal, then each pai…
Reflexive Property
For every real number, the number equals itself. Ex. x=x
Midpoint Theorem
If M is the midpoint of line AB, then line AM is congruent to…
16 terms
Geometry Theorems
Theorem 5-3
Proof for Theorem 5-3
Theorem 5-4
Proof for Theorem 5-4
Given an isoceles triangle PQR with line segment PQ is equal…
...
...
...
Theorem 5-3
Given an isoceles triangle PQR with line segment PQ is equal…
Proof for Theorem 5-3
...
Geometry - Theorems
Theorem 1
Theorem 2
Theorem 3
Theorem 4
Congruent complements measure 45 degrees
Complements of congruent angles are congruent
Supplements of the same angle are congruent
Two lines parallel to the same line are parallel to each other
Theorem 1
Congruent complements measure 45 degrees
Theorem 2
Complements of congruent angles are congruent
65 terms
Geometry Theorems
Theorem 2.1 (Congruent Supplements Thm.)
Theorem 2.2 (Congruent Complements Thm.)
Theorem 2.3 (Vertical Angles Thm.)
Theorem 3.1 (Transitivity of Parallel…
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 are vertical angles, then they are congruent.
If two lines are parallel to the same line, then they are par…
Theorem 2.1 (Congruent Supplements Thm.)
If two angles are supplementary to the same angle or to congr…
Theorem 2.2 (Congruent Complements Thm.)
If two angles are complementary to the same angle or to congr…
7 terms
Geometry Theorems
Perpendicular Bisector Thm
Conv. of Perpendicular Bisector Thm
Angle Bisector Thm
Conv. of Angle Bisector Thm
If a point is on the perpendicular bisector of a segment, the…
If a point is equidistant from the endpoints of a segment, th…
If a point is on the bisect of an angle, then it's equidistan…
If a point in the interior of an angle is equidistant from th…
Perpendicular Bisector Thm
If a point is on the perpendicular bisector of a segment, the…
Conv. of Perpendicular Bisector Thm
If a point is equidistant from the endpoints of a segment, th…
14 terms
Geometry Theorems
angle theorem
angle theorem
angle theorem
angle theorem
if 2 angles are supplementary to the same angle then they are…
if two angles are supplementary to congruent angles then they…
if two angles are complementary to the same angle then they a…
if two angles are complementary to congruent angles then they…
angle theorem
if 2 angles are supplementary to the same angle then they are…
angle theorem
if two angles are supplementary to congruent angles then they…
Geometry theorems
Theorem 1-1
Theorem 1-2
Theorem 1-3
Midpoint theorem
If two lines intersect then they intersect in exactly one point
Through a point and a point not on that line there is exactly…
If two lines intersect, then exactly one plane contains the l…
If M is the midpoint of segment AB the AM= 1/2AB and MB=1/2AB
Theorem 1-1
If two lines intersect then they intersect in exactly one point
Theorem 1-2
Through a point and a point not on that line there is exactly…
13 terms
GEOMETRY THEOREMS
Corresponding Angles Posulate
Alternate Interior Angles postulate
Consecutive Interior Angles Postulate
Alternate Exterior Angles postulate
if two lines are cut by a transversal, then the pairs of C.A.…
if two lines are cut by a transversal, then the pairs of A.I.…
if two lines are cut by a transversal, then the pairs of A.E.…
if two lines are cut by a transversal, then the pairs of C.I.…
Corresponding Angles Posulate
if two lines are cut by a transversal, then the pairs of C.A.…
Alternate Interior Angles postulate
if two lines are cut by a transversal, then the pairs of A.I.…
15 terms
Geometry theorems
Cpctc
Reflexive
Hypotenuse leg
Hypotenuse
Corresponding parts of congruent triangles are congruent
A value is equal to itself
If the hypotenuse and a leg of a right triangle are congruent…
the longest side of a right triangle, opposite the right angle
Cpctc
Corresponding parts of congruent triangles are congruent
Reflexive
A value is equal to itself
49 terms
Geometry Theorems
Line intersection theorem
Linear pair theorem
vertical angles theorem
parallel lines and slope theorem
...
...
...
...
Line intersection theorem
...
Linear pair theorem
...
12 terms
Geometry theorems
If two angles are supplementary to the…
If two angles are complementary to the…
If two angles are supplementary to con…
If two angles are complementary to con…
...
...
...
...
If two angles are supplementary to the…
...
If two angles are complementary to the…
...
Geometry Theorems
If two angles are right angles, then t…
If two angles are straight angles, the…
If a conditional statement is true, th…
If angles are supplementary to the sam…
...
...
...
...
If two angles are right angles, then t…
...
If two angles are straight angles, the…
...
18 terms
Geometry Theorems
1
2
3
4
If two angles are right angles, then they are congruent
If two angles are straight angles then they are congruent
If a conditional statement is true, then the contrapositive o…
If angles are supplementary to the same angle, then they are…
1
If two angles are right angles, then they are congruent
2
If two angles are straight angles then they are congruent
23 terms
Geometry Theorems
Right Angle
Congruent angles
Congruent Straight Angles
Bisecting
If an angle is a right angle, then its meausre is 90°
If two angles have the same measure, then they are congruent
If two angles are straight angles, then they are congruent
If a line bisects an angle, then the two angles formed are co…
Right Angle
If an angle is a right angle, then its meausre is 90°
Congruent angles
If two angles have the same measure, then they are congruent
17 terms
Geometry Theorems
theorem 1
theorem 2
theorem 3
theorem 4
if two angles are right angles, then they are congruent
if two angles are straight angles, then they are congruent
if a conditional statement is true, then the contrapositive o…
if angles are supplementary to the same angle, then they are…
theorem 1
if two angles are right angles, then they are congruent
theorem 2
if two angles are straight angles, then they are congruent
11 terms
Geometry Theorems
1-1
1-2
1-3
2-1
If two lines intersect, they intersect in exactly one point.
Through a line and a point not in that line, there is exactly…
If two lines intersect, then exactly one plane contains the l…
If M is the midpoint on segment AB, then AM = 1/2 AB and MB =…
1-1
If two lines intersect, they intersect in exactly one point.
1-2
Through a line and a point not in that line, there is exactly…
Geometry Theorems
Theorem 9-4
Theorem 9-5
Theorem 9-6
Theorem 9-7
1) congruent arcs have congruent chords... 2) congruent chords h…
A diameter that is perpendicular to a chord bisects the chord…
In the same circle or congruent circles:... 1) chords equally di…
The measure of an inscribed angle is equal to half the measur…
Theorem 9-4
1) congruent arcs have congruent chords... 2) congruent chords h…
Theorem 9-5
A diameter that is perpendicular to a chord bisects the chord…
20 terms
Geometry theorems
~ ( ~p) <=> p... 2 negatives make a posit…
p <=> p v p... p <=> p ^ p
p v q <=> q v p... p ^ q <=> q ^ p... Switch…
(p v q) v r <=> p v (q v r)... (p ^ q) ^…
double negation
simplification
communitive theroms
associative theroms
~ ( ~p) <=> p... 2 negatives make a posit…
double negation
p <=> p v p... p <=> p ^ p
simplification
34 terms
Geometry Theorems
Linear Pair Theorem
Vertical Angles Theorem
Corresponding Angles Theorem
Alt. Interior Angles Theorem
If two angles form a linear pair then add up to 180 degrees
If two angles are vertical then they are congruent
If 2 parallel lines cut by a transversal form 2 corresponding…
If 2 parallel lines cut by a transversal form 2 alt. interior…
Linear Pair Theorem
If two angles form a linear pair then add up to 180 degrees
Vertical Angles Theorem
If two angles are vertical then they are congruent
6 terms
Theorems (Geometry)
1
2
3
4
If two angles form a right angle, then they are complementary
If two angles form a linear pair, then they are supplementary
If two angles are complements of the same angle, then they ar…
If two angles are congruent, then their complements are congr…
1
If two angles form a right angle, then they are complementary
2
If two angles form a linear pair, then they are supplementary
18 terms
Geometry Theorems
Theorem 1
Theorem 2
Theorem 3
Theorem 4
If two angles are right angles, then they are congruent (Righ…
If two angle are straight angles, then they are congruent (St…
If a conditional statement is true, then its contrapositive i…
If angles are supplementary to the same angle, then they are…
Theorem 1
If two angles are right angles, then they are congruent (Righ…
Theorem 2
If two angle are straight angles, then they are congruent (St…
14 terms
Geometry Theorems
IAT
SIAT
DIAT
CQT
inscribed angle theorem (two inscribed angles subtending same…
sector inscribed angle theorem (a sector angle subtending the…
diameter inscribed angle theorem (an inscribed angle subtende…
cyclic quadrilateral theorem (opposite angles of a cyclic qua…
IAT
inscribed angle theorem (two inscribed angles subtending same…
SIAT
sector inscribed angle theorem (a sector angle subtending the…
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