Math Theorems Ch 4-6

The composition of two (or more) rigid motions is a rigid motion

• Composition theorem

• reflections in parallel lines theorem

• reflections in intersecting lines theorem

• triangle sum theorem

If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is the same as a translation.

• exterior angle theorem

• reflections in parallel lines theorem

• reflections in intersecting lines theorem

• triangle sum theorem

If lines k and m intersect at point p, then a reflection in line k followed by a reflection in line m is the same as a rotation about point p. The angle of rotation is 2x, where x is the measure of the acute or right angle formed by lines k and m.

• exterior angle theorem

• corollary to the triangle sum theorem

• Reflections in intersecting lines theorem

• triangle sum theorem

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

• exterior angles theorem

• corollary to the triangle sum theorem

• properties of triangle congruence

• Triangle sum theorem

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

• exterior angles theorem

• corollary to the triangle sum theorem

• properties of triangle congruence

• third angles theorem

The acute angles of a right triangle are complementary

• SAS congruence theorem

• corollary to the triangle sum theorem

• properties of triangle congruence

• third angles theorem

Reflexive: triangle ABC = triangle ABC

Symmetric: If triangle ABC = triangle DEF, then triangle DEF = triangle ABC

Transitive: if triangle ABC = triangle DEF, and triangle DEF = triangle JKL, the triangle ABC = triangle JKL

• SAS congruence theorem

• base angles theorem

• Properties of triangle congruence

• third angles theorem

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

• SAS congruence theorem

• base angles theorem

• converse of the base angles theorem

• Third angles theorem

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent

• SAS congruence theorem

• base angles theorem

• converse of the base angles theorem

• corollary to the base angles theorem

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

• corollary to the converse of the base angles theroem

• base angles theorem

• converse of the base angles theorem

• corollary to the base angles theorem