Proving Congruent Angles Skill 13 a Objective HSGCO

Proving Congruent Angles Skill 13 a

Objective HSG-CO. 9: Students are responsible for understanding and applying theorems about angles.

Theorem 1; Vertical Angles Theorem Prove that vertical angles are congruent. 1) Given 2) Def. of Linear Pair 3) Linear Pair Post. 4) Def. of supplementary 5) Transitive Prop. 1 2 3 6) Subtraction Prop. Q. E. D.

Theorem 2; Congruent Supplements Theorem If two angles are supplements of the same angle, then the two angles are congruent. Statement Reason 1) Given 2) Definition of supplementary 3) Transitive Prop. 4) Subtraction Prop. 3 1 2 Q. E. D.

Theorem 3 Congruent Complements Theorem If two angles are complements of the same angle, or of congruent angles, then the two angles are congruent. 1 If 2 3

Theorem 4 Congruence of Right Angles Theorem All right angles are congruent. 1 2

Theorem 5 Angles Congruent/Supplementary Theorem If two angles are congruent and supplementary, the each is a right angle. 1 2

Example 1; Using Vertical Angles a) What is the value of x? b) What is the value of x?

Example 2; Proofs using Thm. 1 Statement Reason 1) Given 2) Vertical Angles Theorem 3) Transitive Prop. 12 43 4) Vertical Angles Theorem 5) Transitive Prop. Q. E. D.

Example 2; Proofs using Thm. 1 Statement Reason 1) Given 2) Vertical Angles Theorem 3) Transitive Prop. 4) Transitive Prop. Q. E. D. 12 43

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