standard 2.0, 4.0. angles formed by opposite rays

Standard 2.0, 4.0

Angles formed by opposite rays.

Angles that share a common side and a common vertex, but have no common interior points.

Two angle whose measures have a sum of 90 degrees.

or

Two angles whose measures have a sum of 180 degrees.

or ?135

Name a pair of vertical angles.

Name a pair of adjacentAngles.

Name a pair of complementary angles.

Name a pair of supplementary angles.

Prove that EVERY pair of vertical angles is congruent by proving that 2 4.

Statement ReasonAngles 1, 2, 3, and 4 created by intersecting lines Given

Angle 2 and 4 are vertical. Definition of vertical angles.Angle 2 and 3 make a straight angle.Angle 3 and 4 make a straight angle. Definition of straight angle.

m2 + m3 = 180 m3 + m 4 = 180

Angle Addition Postulate

m2 + m3 = m3 + m 4 Substitution

m2 = m 4 Subtraction property of Equality

QED

Theorem 2.1: All vertical angles are congruent!

If two angles are complementary to the same angle (or congruent angles), then the two angles are congruent.

If two angles are supplementary to the same angle (or congruent angles), then the two angles are congruent.

All right angles are congruent.

m∠1

m∠2

m∠3

m∠4

Homework

Page 112-113#1-3, 10, 12-18 & 30-32