Presentation on theme: "Proving Angles Congruent"— Presentation transcript:
1 Proving Angles Congruent An Introduction to Geometric Proofs
2 ProofIs a set of deductive steps which are used to show that a conditional statement (or “Theorem”) is true. Each step is justified by a)postulate,) property,)definition,)algebraic rules (“Simplify”),) previously proved theorem or)as “Given” information
3 In a Paragraph Proof…Each step and reason is written as a sentence in a paragraph.“Given” info is explicitly stated or shown in a diagram* “Prove” the conclusion of the conditional; it is the last part of the proof.
5 Congruent Supplements Theorem If 2 angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
6 Congruent Complements Theorem If 2 angles are complements of the same angle (or of congruent angles), then the two angles are congruent.Draw a picture…..Given:Prove:
7 Paragraph Proof By definition of congruence, By definition of complementary angles,_____________________________By substitution (or transitive p of =),____________________________By subtraction p of =, ___________By definition of congruence,q.e.d.! (quod est demonstratum)
8 All Right Angles are Congruent Draw a picture…Given…..Prove…..
9 Paragraph Proof By definition of right angles, _________________________By substitution (or transitive p of =),____________________________By definition of congruence, ________________________q.e.d.! (quod est demonstratum)
10 If two angles are congruent and supplementary, then each is a right angle. Draw a picture…Given…..Prove…..
11 Paragraph Proof By definition of congruent angles, __________________________By definition of supplementary angles,____________________Substituting one angle measure for the other yields______________Which then simplifies into ________.Use the division p of = to get____________.Because the angles are congruent, ________________ and by the definition of right angles, both angles must be_____________q.e.d!