Essential Question How can you prove a mathematical statement? A proof is a logical argument that uses deductive reasoning to show that a statement is true
Algebraic Proof Going Deeper Essential question: What kinds of justifications can you use in writing algebraic and geometric proofs? PHÉP HON CC9-12
Holt McDougal Geometry 2-5 Algebraic Proof Warm Up Solve each equation 1 3x + 5 = 17 2 r – 3 5 = 8 7 3 4t – 7 = 8t + 3 4 5 2(y – 5) – 20 = 0
2-5 When writing algebraic proofs in geometry, you can also use definitions Possible answer: The Substitution Property states that if a b, then b can
Fill in the blanks to find the answer 2-35 Holt McDougal Geometry 4 /2= t3 U b 5 lna proof, each step in the proof is on the left and
2-5 Properties of Equality Addition Subtraction Reteach When writing algebraic proofs in geometry, you can also use definitions, postulates,
2 5 - Proofs About Angle Pairs and Segments (Part 1) Given: PQ = RS 3 PQ+QR = PR 4 RS+QRQS 5 PR=QS 2) Given:
ovals, not the answer Angles Theorem with geometry software You can complete proofs of Theorems 2-4 and 2-5 in Exercises 14 and 21, respectively
Holt Geometry All rights reserved Fill in the blanks to find the answer 2-5 Practice A Algebraic Proof A Addition Property of Equality
x = 12 d 3 4 5 6 Write a two-column proof:
2 EXPLORATION: Writing Steps in a Proof Work with a partner Six steps of a proof are Given mZ1 = m23 Prove mZEBA = mZCBD 54 Geometry Student Journal 5 mZ1 + m22 = MLCBD 5 Angle Addition Postulate (Post 1 4) 6 MLEBA = MLCBD 6 Transitive Property of Equality Communicate Your Answer 3
2-5 Algebraic Proof Going Deeper Essential question: What kinds of justifications can you undefined terms, postulates are basic building blocks of geometry 5 Symmetric Prop of = Answers 6 Reflexive Prop of = Additional Practice 7
Communicate Your Answer 3 How can To be proficient in math, you need to In a two-column proof, each statement in the left-hand column is either given 5 m∠DBA = m∠EBC 5 Transitive Property of Equality Monitoring Progress
Holt McDougal Geometry 2-5 Algebraic Proof Example 2 Continued 1 Understand the Problem The answer will be the temperature in degrees Fahrenheit
PERIOD Chapter 2 34 Glencoe Geometry Explain how the figure illustrates that each statement is true Then state the postulate that can be used to show
2-6 Geometric Proof Hypothesis To write a geometric proof, start with the 2 given 3 PNENM 3 det, of midpoint 4 PQENM 4 given 5 PN=PQ 5