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Geometry Theorems/Postulates/Definition/Properties
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Gravity
Terms in this set (64)
Perpendicular Transversal Theorem
In a plane, if a line, or transversal, is perpendicular to one of two parallel lines, then it is perpendicular to the other line
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
CPCTC
Corresponding parts of congruent triangles are congruent
Third Angle Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent
Perimeters of Similar Polygons Theorem
If two polygons are similar, then their perimeters are proportional to the scale factor between them
Angle Sum Theorem
The sum of the interior angles of any triangle is 180 degrees
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
SSS Congruence Postulate
If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent
SAS Congruence Postulate
If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
ASA Congruence Postulate
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
AAS Congruence Postulate
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
SSS Similarity Theorem
If all pairs of corresponding sides of two triangles are proportional, then the triangles are similar
SAS Similarity Theorem
If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides into segments of proportional lengths
Triangle Mid-Segment Theorem
A mid-segment is parallel to one side of the triangle, and it's length is half the length of that side
Isosceles Triangle Theorem
If two sides of a triangle are congruent, the angles opposite of them are congruent
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, the sides opposite of them are congruent
Exterior Angle Inequality Theorem
The measure of the exterior of a triangle is greater than the measure of either of its corresponding remote interior angles
Perpendicular Bisector Theorem
If a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of the segment, then it is on the perpendicular bisector of the segment
Circumcenter Theorem
The circumcenter is equidistant from the vertices of a triangle
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle
Converse of the Angle Bisector Theorem
If a point is in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle
Incenter Theorem
The incenter is equidistant from the sides of the triangle
Corresponding Angles Postulate
If two lines are parallel, then the corresponding angles are congruent
Alternate Interior Angles Theorem
If two lines are parallel, then the alternate interior angles are congruent
Alternate Exterior Angles Theorem
If two lines are parallel, then the alternate exterior angles are congruent
Consecutive Interior Angles Theorem
If two lines are parallel, then the consecutive interior angles = 180 degrees
Converse of the Corresponding Angles Postulate
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel
Converse of the Alternate Interior Angles Theorem
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel
Converse of the Alternate Exterior Angles Theorem
If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel
Converse of the Consecutive Interior Angles Theorem
If two lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel
Reflexive Property
A quantity is congruent to itself
Symmetric Property
If a = b, then then b = a
Transitive Property
If a =b and b = c, then a = c
Addition Property
If equal quantities are added to equal quantities, the sums are equal
Subtraction Property
If equal quantities are subtracted from equal quatities, the differences are equal
Multiplication Property
If equal quantities are multiplied by equal quantities, the products are equal
Division Property
If equal quantities are divided by equal quantities, the quotients are equal
Substitution Property
A quantity may be substituted for its equal in any expression
Distributive Property
If a(b+c) then ab + ac
Angle Addition Postulate
If D is a point in the interior of angle ABC then the measure of ABD + the measure of DBC = the measure of ABC
Definition of Congruent Segments
Segments are congruent if their measures are equal
Definition of Congruent Angles
Angles are congruent if their measures are equal
Complement Theorem
If the non-common sides of two adjacent angles form a right angle, then the angles are complementary angles
Definition of Midpoint
If a point is the midpoint of a segment, then it divides the segment into two congruent parts
Definition of Angle Bisector
If a ray (or line) is an angle bisector, then it divides the angle into two congruent angles
Definition of Segment Bisector
If a line is a segment bisector, then it divides the segment into two congruent segments
Definition of Complementary
If two angles are complementary, then their measures add up to 90 degrees
Definition of Supplementary
If two angles are supplementary, then their measures add up to 180 degrees
Definition of Perpendicular
If lines are perpendicular, then they create 90 degree angles
Congruent Supplements Theorem
Supplements of the same angle, or congruent angles, are congruent
Congruent Complements Theorem
Complements of the same angle, or congruent angles, are congruent
Definition of Linear Pair
A pair of adjacent angles formed whose non-common sides are opposite rays
Linear Pair Theorem (Supplement Theorem)
If two angles form a linear pair, then they are supplementary
Definition of Vertical Angles
Angles opposite each other formed when two lines intersect
Vertical Angles Theorem
If two angles are vertical angles, then they are congruent
Triangle Sum Theorem
The sum of the interior angles of a triangle is 180 degrees
Centroid Theorem
The centroid is two-thirds of the distance from each vertext to the midpoint of the opposite side
7.8 Theorem (can't use as name of theorem)
Similar triangles have corresponding altitudes proportional to corresponding sides
7.9 Theorem (can't use as name of theorem)
Similar triangles have corresponding angle bisectors proportional to corresponding sides
7.10 Theorem (can't use as name of theorem)
Similar triangles have corresponding medians proportional to corresponding sides
Triangle Angle Bisector Theorem
An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides
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