Chapter 2 Section 5. Objective Students will make a connection between reasoning in Algebra and...
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Transcript of Chapter 2 Section 5. Objective Students will make a connection between reasoning in Algebra and...
![Page 1: Chapter 2 Section 5. Objective Students will make a connection between reasoning in Algebra and reasoning in Geometry.](https://reader036.fdocuments.in/reader036/viewer/2022082612/56649f1e5503460f94c3505b/html5/thumbnails/1.jpg)
REASONING IN ALGEBRA AND GEOMETRY
Chapter 2 Section 5
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Objective
Students will make a connection between reasoning in Algebra and reasoning in Geometry.
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Properties of Equality
Algebraic properties of equality are used in geometry to justify steps to solving problems.
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Properties of Equality
Addition Property If A = B then A + C = B + C
Subtraction Property If A = B then A – C = B – C
Multiplication Property If A = B then A · C = B · C
Division PropertyIf A = B then A ÷ C = B ÷ C (iff C ≠ 0)
![Page 5: Chapter 2 Section 5. Objective Students will make a connection between reasoning in Algebra and reasoning in Geometry.](https://reader036.fdocuments.in/reader036/viewer/2022082612/56649f1e5503460f94c3505b/html5/thumbnails/5.jpg)
Properties of Equality
Reflexive Property A = A
Symmetric Property If A = B, then B = A
Transitive Property If A = B and B = C, then A = C
Substitution Property If A = B, then A can replace B in any
expression.
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Distributive Property
A ( B + C ) = AB + AC
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Page 114
Look at Problem 1
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Properties of Congruence
Reflexive, Symmetric, and Transitive properties hold true for congruence the same as they do for equivalence.
(See page 114 for examples of congruence properties).
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Proof
A convincing argument that uses deductive reasoning
It logically shows why a conjecture is true.
![Page 10: Chapter 2 Section 5. Objective Students will make a connection between reasoning in Algebra and reasoning in Geometry.](https://reader036.fdocuments.in/reader036/viewer/2022082612/56649f1e5503460f94c3505b/html5/thumbnails/10.jpg)
Two-column Proof
Lists each statement (or step) on the left and gives the justification on the right.
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Page 116
Look at Problem 3. Try the “Got It’ Problem 3.