Warm Up Rewrite each term using math symbols you learned in chapter 1 (symbols for a line, angle, ray, etc.) Example: MN Ray MN _________________________________________________________.

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Presentation transcript:

Warm Up Rewrite each term using math symbols you learned in chapter 1 (symbols for a line, angle, ray, etc.) Example: MN Ray MN _________________________________________________________ Angle ABC ___________________________________________ Line segment JK _________________________________________ Congruent ___________________________________________ Length of line segment with endpoints Y and Z _________________

Algebraic Reasoning and Proofs (part 2) Chapter 2.4

To recap: A proof is like a story, where the order is VERY important One type of math proof is a 2-column proof. It has: Statements on left Reasons on right We reviewed Algebraic Properties as “reasons” in math proofs: Addition property of equality Subtraction property of equality Multiplication property of equality Division property of equality Substitution property of equality Distributive property

Other Properties of Equality Reflexive Property of Equality Reflexive property examples: BD = BD x = x < ABC = < ABC

Other Properties of Equality Symmetric Property of Equality Symmetric property examples: If x = y, then y = x

Other Properties of Equality Transitive Property of Equality Transitive property examples: If BC = XY and XY = 8, Then BC = 8

Which property? Copy the statements below. Use the property given to complete each one. 20 + CD Substitution Property of Equality: If AB = 20, then AB + CD = ___________. m∠2 = m∠1 Symmetric Property of Equality: If m∠1 = m∠2, then ______________. m∠1 = m∠3 Transitive Property of Equality: If m∠1 = m∠2 and m∠2 = m∠3, then ____________________________. m∠ABC Reflexive Property of Equality: m∠ABC = ________________.

Reasons to be used in proofs Addition Property of Equality (Add Prop. Equality) Subtraction Prop. Equality Multiplication Prop. Equality Division Prop. Equality Substitution Prop. Equality Distributive Prop. Reflexive Property Symmetric Property Transitive Property Definition of complementary angles Definition of supplementary angles Definition of angle bisector or segment bisector Definition of congruent segments or angles Definition of midpoint