2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will...
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Transcript of 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will...
![Page 1: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/1.jpg)
2.5 Reasoning in Algebra and Geometry
• Algebraic properties of equality are used in Geometry.– Will help you solve problems and justify each step.
• In Geometry, you accept postulates and properties as true.– Some of the properties you accept as true are the
properties of equality from Algebra.
![Page 2: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/2.jpg)
Properties of Equality• Let a, b, and c be any real numbers.
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 Property: If a = b and c ≠ 0, then a/c = b/c.
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 b can replace a in any expression.
![Page 3: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/3.jpg)
Distributive Property
• Use multiplication to distribute a to each term of the sum or difference within the parentheses.
Sum: a (b + c) = ab + ac
Difference: a (b – c) = ab – ac
![Page 4: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/4.jpg)
Justifying Steps when Solving an Equation• What is the value of x? Justify each step.
![Page 5: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/5.jpg)
Justifying Steps when Solving an Equationangles that form a linear
pair are suppl.
def. of supplementary angles
Substitution Property
Simplify
Subtraction Property of Equality
Division Property of Equality
sup .AOMand MOCare pl
180m AOM m MOC
(2 30) 180x x 3 30 180x
3 150x
50x
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Properties of Congruence
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Using Properties of Equality and Congruence• What is the name of the property of equality or
congruence that justifies going from the first statement to the second statement?
A. 2x + 9 = 19
2x = 10
B.
C.
O Wand W L O L
m E m T m T m E
Subtraction Property of Equality
Transitive Prop. Of Congruence
Symmetric Property of Equality
![Page 8: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/8.jpg)
Proof
• A proof – a convincing argument that uses deductive reasoning.– Logically shows why a conjecture is true.– A two-column proof lists each statement on
the left and the reasons on the right.– Each statement must follow logically from the
steps before it.
![Page 9: 2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,](https://reader033.fdocuments.in/reader033/viewer/2022051515/55143d18550346494e8b474d/html5/thumbnails/9.jpg)
Proof
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Writing a Two-Column Proof
• Write a two-column proof.
Given:
Prove:
1 3m m
m AEC m DEB
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Writing a Two-Column Proof
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More Practice!!!!!
• Homework – p. 117 – 118 # 5 – 19 ALL.