Vertical Angles Theorem

i got this from a geometry book

Theorem 1-1

Vertical Angles Theorem

Vertical angles are congruent.

Theorem 1-2

Congruent Supplements Theorem

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

Theorem 1-3

Congruent Complements Theorem

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

Theorem 2-1

Triangle Angle-Sum Theorem

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

Theorem 2-2

Exterior Angle Theorem

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

Theorem 2-3

Polygon Interior Angle-Sum Theorem

The sum of the measures of the interior angles of an n-gon is (n-2) 180.

Theorem 2-4

Polygon Exterior Angle-Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Theorem 2-5

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

Theorem 2-6

In a plane, two lines perpendicular to a third line are parallel to each other.

Theorem 3-1

A composition of reflections in two parallel lines is a translation.

Theorem 3-2

A composition of reflections in two intersecting lines is a rotation.

Theorem 3-4

Isometry Classification Theorem

There are only four isometries. They are reflection, translation, rotation, and glide reflection.

Theorem 4-1

Isosceles Triangle Theorem

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

Theorem 4-2

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Theorem 4-3

Converse of the Isosceles Triangle Theorem

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

Theorem 4-4

If a triangle is a right triangle, then the acute angles are complementary.

Theorem 4-5

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

Theorem 4-6

All right angles are congruent.

Theorem 4-7

If two angles are congruent and supplementary, then each is a right angle.

Theorem 4-8

Triangle Midsegment Theorem

If a segment joins the midpoint of two sides of a triangle, then the segment is parallel to the third side and half its length.

Theorem 4-9

Triangle Inequality Theorem

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

Theorem 4-10

If two sides of a triangle are not congruent, then the larger angle lies opposite the larger side.

Theorem 4-11

If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.