Geometry Theorems/postulates/collaries

Front 1

Theorem 3-1:

Back 1

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

Front 2

Theorem 3-2:

Back 2

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

Front 3

Theorem 3-3:

Back 3

If two parallel lines are cut by a transversal, then same side interior angles are supplementary.

Front 4

Theorem 3-4:

Back 4

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.

Front 5

Theorem 3-5:

Back 5

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

Front 6

Theorem 3-6:

Back 6

If two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel.

Front 7

Theorem 3-7:

Back 7

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

Front 8

Theorem 3-8:

Back 8

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

Front 9

Postulate 10:

Back 9

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

Front 10

Postulate 11:

Back 10

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

Front 11

Theorem 3-9:

Back 11

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

Front 12

Theorem 3-10:

Back 12

Two lines parallel to a third line are parallel to each other.

Front 13

Theorem 3-11:

Back 13

The sum of the measures of the angles of a triangle are 180 degrees.

Front 14

Theorem 3-11 corollary 1:

Back 14

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

Front 15

Theorem 3-11 corollary 2:

Back 15

Each angle of an equiangular triangle has a measure of 60 degrees.

Front 16

Theorem 3-11 corollary 3:

Back 16

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

Front 17

Theorem 3-11 corollary 4:

Back 17

The acute angles of a right triangle are complementary.

Front 18

Theorem 3-12:

Back 18

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

Front 19

Theorem 3-13:

Back 19

The sum of the measures of the angles of a convex polygon with n sides is (n-2)180.

Front 20

Theorem 3-14:

Back 20

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