Study sets matching "geometry theorems"
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Within a circle or in congruent circles
Diameter & Chord Theorem
Inside parts
Outer whole
Chords equidistant from the center are congruent. Congruent ch…
A diameter that is perpendicular to a chord, bisects the chord…
A•b=c•d
(W+x)x=(y+z)z
Within a circle or in congruent circles
Chords equidistant from the center are congruent. Congruent ch…
Diameter & Chord Theorem
A diameter that is perpendicular to a chord, bisects the chord…
If 2 triangles have 3 pairs of congruen…
If 2 triangles have 2 pairs of congruen…
If a segment/angle is added to congruen…
If a segment/angle is subtracted from c…
Side, Side, Side
Side, Angle, Side
Segment/Angle Addition
Segment/Angle Subtraction
If 2 triangles have 3 pairs of congruen…
Side, Side, Side
If 2 triangles have 2 pairs of congruen…
Side, Angle, Side
Theorem
Theorem
Theorem
Theorem
Vertical angles are congruent.
The angles in a linear pair are supplementary.
Congruence of segments and angles is reflexive, symmetric, and…
All right angles are congruent.
Theorem
Vertical angles are congruent.
Theorem
The angles in a linear pair are supplementary.
Pythagorean Theorem
Linear Pair Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
In a right triangle, the sum of the squares of the lengths of…
If two angles form a linear pair, then they are supplementary.
If two angles are supplementary to the same angle (or to two c…
If two angles are complementary to the same angle (or to two c…
Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of…
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary.
Linear Pair Postulate
Vertical Angles
Right Angle Congruence
Congruent Supplements
If two angles form a linear pair, then they are supplementary.…
Vertical angles are congruent. <1 is congruent to <3 and <2 is…
All right angles are congruent
If two angles are supplementary to the same angle (or to congr…
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.…
Vertical Angles
Vertical angles are congruent. <1 is congruent to <3 and <2 is…
Ruler postulate
Segment addition postulate
Protractor postulate
Angle addition postulate
The points on a line can be put into a one-to-one corresponden…
If B is between A and C, then AB+BC = AC
Given AB and a point O on AB, all rays that can be drawn from…
If S is in the interior of angle PQR, the the measure of angle…
Ruler postulate
The points on a line can be put into a one-to-one corresponden…
Segment addition postulate
If B is between A and C, then AB+BC = AC
Linear Pair Theorem
Vertical Angles Theorem
Parallel Lines and Slopes Theorem
Transitivity of Parallelism Theorem
If two angles form a linear pair, then they are supplementary.
If two angles are vertical angles, then they have equal measur…
Two nonvertical lines are parallel if and only if they have th…
If line x is parallel to line y and line y is parallel to line…
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary.
Vertical Angles Theorem
If two angles are vertical angles, then they have equal measur…
Properties of Segment Congruence
Properties of Angle Congruence
Right Angles Congruence Theorem
Congruent Supplements Theorem
Segment congruence is reflexive, symmetric, and transitive.
Angle congruence is reflexive, symmetric, and transitive.
All right angles are congruent.
If two angles are supplementary to the same angle (or to congr…
Properties of Segment Congruence
Segment congruence is reflexive, symmetric, and transitive.
Properties of Angle Congruence
Angle congruence is reflexive, symmetric, and transitive.
Theorem 1-1
Theorem 1-2
Theorem 1-3
Theorem 1-4
If two lines intersect, then they intersect in exactly one poi…
Through a line and a point not in the line there is exactly on…
If two lines intersect, then exactly one plane contains the li…
...
Theorem 1-1
If two lines intersect, then they intersect in exactly one poi…
Theorem 1-2
Through a line and a point not in the line there is exactly on…
vertical angle theorem
segment bisector
reflexive property of congruence
triangle angle-sum theorem
if two angles are vertical angles, then they are congruent
a line, ray or segment which cuts another line segment into tw…
a quantity is congruent in itself
the sum of the measures of the angle of a triangle are 180 deg…
vertical angle theorem
if two angles are vertical angles, then they are congruent
segment bisector
a line, ray or segment which cuts another line segment into tw…
Linear Pair Theorem
Vertical Angle Theorem
Corresponding Angles Theorem
Alternate Exterior Angles Theorem
If two angles are a linear pair of angles, then their measures…
If two angles are vertical angles, then they are congruent.
If two+ parallel lines are cut by a transversal, then correspo…
If two+ parallel lines are cut by a transversal, then alternat…
Linear Pair Theorem
If two angles are a linear pair of angles, then their measures…
Vertical Angle Theorem
If two angles are vertical angles, then they are congruent.
1-1 Theorem
1-2 Theorem
1-3 Theorem
2-1 Theorem = Midpoint Theorem
If two lines intersect, then they intersect in exactly one poi…
Through a line and a point not in the line there is exactly on…
If two lines intersect, then exactly one plane contains the li…
If M is the midpoint of line AB, then AM = 1/2 AB and MB = 1/2…
1-1 Theorem
If two lines intersect, then they intersect in exactly one poi…
1-2 Theorem
Through a line and a point not in the line there is exactly on…
Congruent Circles Theorem
Congruent Central Angles Theorem
Similar Circles Theorem
Congruent Corresponding Chords Theorem
Two circles are congruent circles iff they have the same radius
In the same circle, or in congruent circles, two minor arcs ar…
All circles are similar
In the same circle or in congruent circles, two minor arcs are…
Congruent Circles Theorem
Two circles are congruent circles iff they have the same radius
Congruent Central Angles Theorem
In the same circle, or in congruent circles, two minor arcs ar…
Complementary Angles
Supplementary Angles
Corresponding angles
Same side interior angles
Two angles whose measures have a sum of 90°
Two angles whose measures have a sum of 180°
Complementary Angles
Two angles whose measures have a sum of 90°
Supplementary Angles
Two angles whose measures have a sum of 180°
triangle sum theorem
third angles theorem
theorem 4.4
interior angles
the sum of the measures of a triangle is 180
if 2 angles of one triangle are congruent to two angles of a s…
the acute angles of a right triangle are complementary
inside the triangle
triangle sum theorem
the sum of the measures of a triangle is 180
third angles theorem
if 2 angles of one triangle are congruent to two angles of a s…
Polygon Interior Angles Theorem
Interior Angles of a Quadrilateral
Polygon Exterior Angles Theorem
Theorem 8.3
The sum of the measures of the interior angles of a convex n-g…
The sum of the measures of the interior angles of a quadrilate…
The sum of the measures of the exterior angles of a convex pol…
If a quadrilateral is a parallelogram, then its opposite sides…
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-g…
Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a quadrilate…
Vertical Angles Theorem
Corresponding Angles Theorem
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
angles that are opposite each other are congruent
if two parallel lines are cut by a transversal then the pairs…
when two parallel lines are cut by a transversal, the resultin…
if two parallel lines are cut by a transversal, then the pairs…
Vertical Angles Theorem
angles that are opposite each other are congruent
Corresponding Angles Theorem
if two parallel lines are cut by a transversal then the pairs…
Theorem for Linear Pairs
Theorem for congruent supplements
Reflexive theorem
Segment/angle addition
Two linear pair angles are always supplementary.
Supplements of congruent angles are congruent to each other. *…
Every object is congruent to itself when reflected, and all an…
If a segment or angle is added to congruent, overlapping segme…
Theorem for Linear Pairs
Two linear pair angles are always supplementary.
Theorem for congruent supplements
Supplements of congruent angles are congruent to each other. *…
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…
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If 2 angles are vertical angles, then they are congruent.
If 2 angles are right angels, then they are congruent.
If 2 angles are supplementary to the same angle, then they are…
If 2 angles are complementary to the same angle, then they are…
...
If 2 angles are vertical angles, then they are congruent.
...
If 2 angles are right angels, then they are congruent.
Linear Pair Theorem
Congruent Supplements Theorem
Right angle congruence theorem
Congruent complements Theorem
If 2 angles form a linear pair, then they are supplementary
If 2 angles are supplementary to the same angle (or to two con…
All right angles are congruent
If 2 angles are complementary to the same angle (or to two con…
Linear Pair Theorem
If 2 angles form a linear pair, then they are supplementary
Congruent Supplements Theorem
If 2 angles are supplementary to the same angle (or to two con…
Properties of Segment Congruence
Properties of Angle Congruence
Right Angles Congruence Theorem
Congruent Supplements Theorem
Segment congruence is reflexive, symmetric, and transitive.
Angle congruence is reflexive, symmetric, and transitive.
All right angles are congruent.
If two angles are supplementary to the same angle (or to congr…
Properties of Segment Congruence
Segment congruence is reflexive, symmetric, and transitive.
Properties of Angle Congruence
Angle congruence is reflexive, symmetric, and transitive.
Congruent Complements Theorems
Reflexive Theorem
Segment Addition Theorem
Segment Subtraction Theorem
Complements of congruent angles are congruent to each other.
Every object is congruent to itself
If a segment is added to congruent segments the results is con…
If a segment is subtracted to congruent segments the results i…
Congruent Complements Theorems
Complements of congruent angles are congruent to each other.
Reflexive Theorem
Every object is congruent to itself