PROVING ANGLES CONGRUENT THEOREM A true statement that

THEOREM • A true statement that follows as a result of other true statements.

IDENTIFYING ANGLES • Vertical Angles – Two angles whose sides form two pairs of

IDENTIFY THE ANGLES Name a pair of vertical angles. Name a pair of adjacent

THEOREM 2 -5 • If two angles are congruent and supplementary, then each is

PROBLEM 1: USING THE VERTICAL ANGLES THEOREM What is the value of x

PROBLEM 2: PROOF USING THE VERTICAL ANGLES THEOREM STATEMENT Reason

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PROVING ANGLES CONGRUENT

THEOREM • A true statement that follows as a result of other true statements. • All theorems MUST be proven! • Postulates and axioms are used to prove theorems

IDENTIFYING ANGLES • Vertical Angles – Two angles whose sides form two pairs of opposite rays. • Adjacent Angles – Two coplanar angles with a common side, a common vertex, and no common interior points. • Complementary Angles – Two angles whose sum measures 90 o. • Supplementary Angles – Two angles whose sum measures 180 o.

IDENTIFY THE ANGLES Name a pair of vertical angles. Name a pair of adjacent Angles. Name a pair of complementary angles. Name a pair of supplementary angles.

VERTICAL ANGLES THEOREM • 2 1 3 4

CONGRUENT SUPPLEMENTS THEOREM • 1 2 3

CONGRUENT COMPLEMENTS THEOREM • 5 4 6

RIGHT ANGLE THEOREM •

THEOREM 2 -5 • If two angles are congruent and supplementary, then each is a right angle.

PROBLEM 1: USING THE VERTICAL ANGLES THEOREM What is the value of x

What is the value of x

FIND THE VALUE OF BOTH VARIABLES.

FIND THE VALUE OF X.

FIND THE MEASURE OF EACH ANGLE.

FIND THE MEASURE OF EACH ANGLE. •

PROBLEM 2: PROOF USING THE VERTICAL ANGLES THEOREM STATEMENT Reason