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Geometry: 2.4-2.6 Notes NAME_______________________
2.4 Use and understand properties of equality__________________________Date:____________________
Define Vocabulary:
equation
solve an equation
formula
Core Concepts
Algebraic Properties of Equality
Let a, b, and c be real numbers.
Addition Property of Equality Ifa b, then a c b c.
Subtraction Property of Equality Ifa b, then a c b c.
Multiplication Property of Equality Ifa^ ^ b, then^ a^ ^ c^ ^ b^ ^ c c,^ 0.
Division Property of Equality If , then , 0.
a b a b c c c
Substitution Property of Equality If a b, then acan be substituted for b
(or b for a) in any equation or expression.
Examples: Justifying steps. Solve the equations and justify each step.
WE DO YOU DO
Distributive Property
Let a, b, and c be real numbers.
Sum a b c (^) ab ac Difference a b c (^) ab ac
Examples: Using the distributive property. Solve the equations and justify each step.
WE DO YOU DO
Examples: Solve the equation for the given variable.
WE DO YOU DO
9 x 2 y 5;y
s t s
Examples: Solve the real-life problem.
WE DO
The formula for the surface area S of a cone is S r 2 rs,where r is the radius
and s is the slant height. Solve the formula for s. Justify each step. Then find the slant
height of the cone when the surface area is 220 square feet and the radius is 7 feet.
Approximate to the nearest tenth.
2.5 Write two-column proofs.________________________________________Date:____________________
Define Vocabulary:
Proof
Two-column proof
Theorem
Examples: Writing a Two-Column Proof
WE DO YOU DO
Theorem 2.1 Properties of Segment Congruence
Segment congruence is reflexive, symmetric, and transitive.
Reflexive For any segment AB,AB AB.
Symmetric If AB^ CD,thenCD AB.
Transitive If AB CDand CD EF,thenAB EF.
Theorem 2.2 Properties of Angle Congruence
Angle congruence is reflexive, symmetric, and transitive.
Reflexive For any angle A,A A.
Symmetric If A B,thenB A.
Transitive If (^) A Band B C,thenA C.
Examples: Name the property that the statement illustrates.
WE DO YOU DO
a. IfRST TSU and TSU VWX , then RST VWX.
b. IfGH^ ^ JK^ , then^ JK^ GH.
2.6 Vertical angle and Linear pairs.___________________________________Date:____________________
Postulate 2.8 Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
1 and 2 form a linear pair, so 1 and 2 are supplementary
andm 1 m 2 180 .
Theorem 2.6 Vertical Angles Congruence Theorem
Vertical angles are congruent.
Examples: Use the diagram and the given angle measure to find the other three angle measures.
WE DO YOU DO
Examples: Find the value of the variable.
WE DO YOU DO
Assignment
