To complete proofs involving angle theorems

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Presentation transcript:

To complete proofs involving angle theorems Geometry Proofs Obj: To Complete Proofs Involving Segment Theorems To complete proofs involving angle theorems

5 Essential Parts to a Good Proof State the theorem to be proved List the given information If possible draw a diagram to illustrate the given information State what is to be proved Develop a system of deductive reasoning

Deductive Reasoning Definitions & postulates-Statements accepted as true w/o proof Theorem- undefined terms that can be used as truth once they have been proven

Theorem: Congruence of segments is reflexive, symmetric, and transitive Written as symbols: Reflexive: Symmetric: IF , then Transitive: IF and then

Example: 1.) _________ 2.) AD = AB + BD 2.) ___________ C D Given: Prove: Statements Justification 1.) _________ Given 2.) AD = AB + BD 2.) ___________ Seg. + post Seg. + post. 3.) BD = BC + CD 3.)___________ 4.) AD = AB + BC + CD 4.)___________ substitution

Your Turn: Given: pts PQRS are collinear Prove: PQ = PS - QS P Q R S Statement Justification 1.) pts PQRS are collinear 2.) PS = PQ + QS 3.) PS – QS = PQ 4.) PQ = PS - QS

Solution to “Your Turn”: P Q R S Given: pts PQRS are collinear Prove: PQ = PS - QS Statement Justification 1.) pts PQRS are collinear 1.) Given 2.) PS = PQ + QS 2.) Seg. + post 3.) PS – QS = PQ 3.) Subtraction 4.) PQ = PS - QS 4.) symmetric Prop.

Verifying Angle Relationships

Theorems Supplement thm-if 2 angles form a linear pr then they are supplementary Congruence of angles is reflexive, symmetric, and transitive Angles supplementary to the same angle or to congruent angles are congruent

Theorems Continued Angles complementary to the same angle or congruent angles are congruent All right angles are congruent Vertical angles are congruent Perpendicular lines intersect to form 4 right angles

Example: If and are vertical , and . Find Angle A = Angle C, Vert. angles 3x - 2 = 2x + 4 A = 3(6) - 2 -2x +2 -2x +2 = 16o x = 6 C = 2 (6) + 4 = 16o

Your Turn: Find the measure of each numbered angle 1 2 2x - 5 + x - 4 = 180 2 (63) - 5 = 121o 63 - 4 = 59o 3x - 9 = 180 3x = 189 x = 63

Homework: Put this in your agenda: Pg 116 5 – 12, 21 – 24 Pg 128 9 – 21 odd, 22 - 28