Geometry Chapter 3

Thm 3-1

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

Postulate 10

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

Theorem 3-2

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

Theorem 3-3

if two parallel lines are cut by a transversal, then ssi angles are supp

Theorem 3-4

If a transversal is perpendicular to one of two paralllel lines, then it is perpendicular to the other one aso

Postulate 11

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

Theorem 3-5

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

Theorem 3-6

If two lines are cut by a transversal and ssi angles are supp , then the angles are parallel

Theorem 3–7

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

Theorem 3–8

through a point outside a line, there's exactly one line parallel to the given line

Theorem 3–9

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

Theorem 3–10

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

Theorem 3–11

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

Corollary 1

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

Corollary 2

each angle of an equiangular triangle has measure 60

Corollary 3

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

Corollary 4

The acute angles of the right triangle are complementary

Theorem 3–12

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

Theorem 3–13

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

Theorem 3-14

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

Ways to prove two lines parallel

Show that a pair of corresponding angles are congruent, Show that a pair of alternate interior angles are congruent, Show that a pair of the same side interior angles are supplementary, In a plane show that both lines are perpendicular to a third line, show that both lines are parallel to a third line