Advance Geometry Midterm Postulates And Theorems

Front 1

Linear Pair Postulate

Back 1

If two angles form a linear pair, then they are supplementary.

Front 2

Parallel Postulate

Back 2

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Front 3

Perpendicular Postulate

Back 3

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Front 4

Corresponding Angles Postulate

Back 4

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Front 5

Corresponding Angles Converse

Back 5

If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Front 6

Slopes of Parallel Lines

Back 6

Two nonvertical lines are parallel if and only if they have the same slope.

Front 7

Slopes of Perpendicular Lines

Back 7

Two nonvertical lines are perpendicular if and only if the products of their slopes is -1.

Front 8

Side-Side-Side (SSS) Congruence

Back 8

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Front 9

Side-Angle-Side Congruence Postulate

Back 9

If two sides and the included angle of 1 triangle are congruent to two angles and the included side of a second triangle, then the 2 triangles are congruent.

Front 10

Angle-Angle (AA) Similarity

Back 10

If two angles of one triangle are congruent to two angles of another triangle then the two triangles are similar.

Front 11

Reflexive Property of Congruence

Back 11

For any angle/segment AB=AB or <A = <A

Front 12

Symmetric Property of Congruence

Back 12

if AB=BA then BA=AB or <A=<B then <B=<A

Front 13

RIght Angles Congruence Theorem

Back 13

All right angles are congruent

Front 14

Congruent Supplements Theorem

Back 14

If two angles are supplementary to the same angle then the two angles are congruent

Front 15

Congruent Complements Theorem

Back 15

If two angles are complementary to teh same angle then the two angles are congruent

Front 16

Vertical Angles Congruence Theorem

Back 16

Vertical angles are congruent

Front 17

Alternate Interior Angles Theorem

Back 17

If two parallel lines are cut by a transveral then the pairs of alternate interior angles are congruent

Front 18

Alternate Exterior Angles

Back 18

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Front 19

Consecutive Interior Angles Theorem

Back 19

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Front 20

Alternate Interior Angles Converse

Back 20

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

Front 21

Alternate Exterior Angles Converse

Back 21

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.

Front 22

Consecutive Interior Angles Converse

Back 22

If two lines are cut by a transversal so the consecutive interior angles are supplementary, the line are parallel

Front 23

Transitive Property of Parallel Lines

Back 23

If to lines are parallel to the same line then they are parallel to each other.

Front 24

Perpendicular Transversal Theorem

Back 24

If a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other

Front 25

Lines Perpendicular to a Transversal Theorem

Back 25

If two lines are perpendicular to teh same line, then they are parallel.

Front 26

Triangle Sum Theorem

Back 26

The sum of the measures of interior angles = 180

Front 27

Exterior Angle Theorem

Back 27

The measure of an exterior angle of a triangle is equal to teh sum of the measures of the two nonadjacent interior angles.

Front 28

Third Angles Theorem

Back 28

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Front 29

Hypotenuse-Leg (HL) Congruence

Back 29

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle then the two triangles are congruent.

Front 30

Angle-Angle-Side (AAS)

Back 30

If two angles and a non-included side of one triangle are congruent to two angles and teh corresponding non-included side of a second triangle, then the two triangles are congruent

Front 31

Base Angles Theorem

Back 31

If two sides of a triangle are congruent, then the angles opposite them are congruent.

Front 32

Midsegment Theorem

Back 32

THe segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

Front 33

Perpendicular Bisector Theorem

Back 33

If a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front 34

Concurrency of Perpendicular Bisectors

Back 34

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.

Front 35

Circumcenter

Back 35

The point of concurrency of perpendicular bisectors and equidistant from the vertices.

Front 36

Angle Bisector Theorem

Back 36

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Front 37

Concurrency of Angle Bisectors of a Triangle

Back 37

The angle bisectors of a triangle intersect at a pint that is equidistant from the sides of a triangle.

Front 38

Incenter

Back 38

Point of concurrency of angle bisectors and equidistant from the sides of a triangle.

Front 39

Concurrency of Medians of a Triangle

Back 39

The medians of a triangle intersect at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.

Front 40

Centroid

Back 40

Point of concurrency of the medians and is two thirds the distance from each vertex to the midpoint of the opposite side.

Front 41

Concurrency of Altitudes of a Triangle

Back 41

The lines containing altitudes of a triangle are concurrent

Front 42

Orthocenter

Back 42

The point of concurrency of Altitudes

Front 43

Triangle Inequality Theorem

Back 43

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.