Theorems And Postulates

Front 1

No choice theorem

Back 1

If two angles of one triangle are congruent to two angles of a second triangle then the third angles must be congruent.

Front 2

Midline theorem

Back 2

A segment jointing the midpoints of two sides of a triangle is parallel to the 3rd side, and it's length is one half the length of the 3rd side

Front 3

theorem 49

Back 3

if a plane intersects two perpendicular planes, then the lines of intersection are parallel.

Front 4

theorem 49

Back 4

If a line perpendicular to two distinct lines on a plane that lie in a plane and that pass through it's foot, then it is perpendicular to the plane.

Front 5

How to determine a plane

Back 5

three non collinear points determine a plane
a line and a point not in the line determine a plane
two intersecting lines determine a plane
two parallel lines determine a plane

Front 6

Theorem 5

Back 6

If angles are supplementary to congruent angles, then they are congruent

Front 7

Transitive properties

Back 7

If angles or segments are congruent to the same angle or segment, then they are congruent to each other
And
If angles or segments are congruent to congruent angles or segments, then they are congruent to each other

Front 8

HL postulate

Back 8

if there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent

Front 9

Theorem 24

Back 9

if two points are each equidistant from the endpoints of a segment, then to the two points determine the perpendicular bisector of that segment.

Front 10

theorem 25

Back 10

if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment

Front 11

theorem 36

Back 11

if two coplanar lines are perpendicular to a third line, they are parallel.

Front 12

Parallelogram

Back 12

the opposite sides are parallel
the opposite sides are congruent
the opposite angles are congruent
the diagonals bisect each other
any pair of consecutive angles are supplementary

Front 13

rectangles

Back 13

(it is a parallelogram)
All angles are right angles
diagonals are congruent

Front 14

kite

Back 14

two disjoint pairs of consecutive sides are congruent
the diagonals are perpendicular
one of the diagonals is the perpendicular bisector of the other
one of the diagonals bisects a pair of opposite angles
one pair of opposite angles
one pair of opposite angles are congruent

Front 15

Rhombus

Back 15

(it is a parallelogram and a kite-full properties)
all sides are congruent
the diagonals bisect the angles
the diagonals are perpendicular bisectors of each other
the diagonals divide the rhombus into four congruent right triangles

Front 16

Square

Back 16

(all properties of a rectangle and rhombus)
the diagonals form four isosceles right triangles

Front 17

Isosceles Trapezoids

Back 17

The legs are congruent by definition
the bases are parallel
the lower base angles are congruent
the upper base angles are congruent
the diagonals are congruent
any lower base angle is supp. to any upper base angle