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60 Cards in this Set
 Front
 Back
Theorem 11

if two lines intersect, then they intersect in exactly one point


Theorem 12

Through a line and a point not in the line there is exactly one plane


Theorem 13

If two lines intersect, then exactly one plane contains the lines


Theorem 21 (Midpoint Theorem)

If M is the midpoint of (segment) AB, then AM=1/2AB and MB=1/2AB


Theorem 22 (Angle Bisector Theorem)

if (ray) BX is the bisector of angle ABC, then m(angle)ABX=1/2 m(angle)ABC and m(angle)XBC=1/2 m(angle)ABC


Theorem 23

Vertical angles are congruent


Theorem 24

If two lines are perpendicular, then they form congruent adjacent angles


Theorem 25

If two lines form congruent adjacent angles, then the lines are perpendicular


Theorem 26

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary


Theorem 27

If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent


Theorem 28

If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent


Theorem 31

If two parallel planes are cut by a third plane, then the lines of intersection are parallel


Theorem 32

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


Theorem 33

If two parallel lines are cut by a tranversal, then sameside interior angles are supplementary


Theorem 34

if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also


Theorem 35

If two lines are cut by the transversal and alternate interior angles are congruent, then the lines are parallel


Theorem 36

If two lines are cut by a transversal and sameside interior angles are supplementary , then and lines are parallel


Theorem 37

In a plane two lines perpendicular to the same line are parallel


Theorem 38

Through a point outside a line, there is exactly one line parallel to the given line


Theorem 39

Through a point outside a line, there is exactly one line perpendicular to the given line


Theorem 310

two lines parallel to a third line are parallel to each other


Theorem 311

The sum of the measures of the angles of a triangle is 180


Theorem 311 Corollary 1

if two angles of one triangle are congruent to two angles of another triangle, the the third angles are congruent


Theorem 311 Corollary 2

Each angle of an equiangular triangle has measure 60


Theorem 311 Corollary 3

In a triangle, there can be at most one right angle or obtuse angle


Theorem 311 Corollary 4

The acute angles of a right triangle are complementary


Theorem 312

The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles


Theorem 313

The sum of the measures of the angles of a convex polygon with n sides is (n2)180


Theorem 314

The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex is 360


Theorem 41 (Isosceles Triangle Theorem)

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


Theorem 41 Corollary 1

An equilateral triangle is also equiangular


Theorem 41 Corollary 2

An equilateral triangle has three 60 degree angles


Theorem 41 Corollary 3

The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint


Theorem 42

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


Theorem 42 Corollary 1

An equiangular triangle is also equilateral


Theorem 43 (AAS Theorem)

If two angles and a nonincluded side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent


Theorem 44 (HL Theorem)

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent


Theorem 45

If a point lies on the perpendicular bisector of a segment, then the point is equidistant for the endpoints of the segment


Theorem 46

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


Theorem 47

If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle


Theorem 48

If a point is equidistant from the sides of an angle. then the point lies on the bisector of the angle


Theorem 51

Opposite sides of a parallelogram are congruent


Theorem 52

Opposite angles of a parallelogram are congruent


Theorem 53

Diagonals of a parallelogram bisect each other


Theorem 54

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram


Theorem 55

If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram


Theorem 56

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallogram


Theorem 57

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram


Theorem 58

if two lines are parallel, then all points on one line are equidistant from the other line


Theorem 59

If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal


Theorem 510

a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side


Theorem 511

The segment that joins the midpoints of two sides of a triangle
(1) is parallel to the third side (2) is half as long as the third side 

Theorem 512

Diagonals of a rectangle are congruent


Theorem 513

The diagonals of a rhombus are perpendicular


Theorem 514

Each diagonal of a rhombus bisects two angles of the rhombus


Theorem 515

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices


Theorem 516

If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle


Theorem 517

If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus


Theorem 518

Base angles of an isosceles trapezoid are congruent


Theorem 519

The median of a trapezoid
(1) is parallel to the bases (2) has a length equal to the average of the base lengths. 