Download lesson 2.5 Geometry.notebook

lesson 2.5 Geometry.notebook
1)___ p®q
Warm Up ~ Matching!
October 16, 2015
A. Biconditional
B. Law of Syllogism
2)___ If p®q and q®r then p®r C. Law of Detachment
3)___ q®p
D. Inverse
4)___ p«q
E. Conditional
5)___ ~q® ~p
F. Converse
6)___ If p®q is true, and p is true, then q is true.
G. Contrapositive
7)___ ~p® ~q
8. Determine if the biconditional is true. If false give a counterexample.
"A square has a side length of 5 iff it has an area of 25." lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
2­5 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
lesson 2.5 Geometry.notebook
October 16, 2015
2­5 Algebraic Proof
GOALS
1) Review properties of equality and use them to write algebraic proofs.
2) Identify properties of equality and congruence. Definitions~1 total
proof
lesson 2.5 Geometry.notebook
October 16, 2015
2­5 Algebraic Proof
A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.
An important part of writing a proof is giving justifications to show that every step is valid. lesson 2.5 Geometry.notebook
2­5 Algebraic Proof
October 16, 2015
lesson 2.5 Geometry.notebook
1) If x=3 and 3=y, then x=y
2) If x=4 then 4=x
3) 12=12
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
Example 1: Solving an Equation in Algebra
Solve the equation 4m – 8 = –12. Write a justification for each step.
Statement
Reason
lesson 2.5 Geometry.notebook
Your Turn! Example 1
Statement Reason
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
Solve the given equation, justify each step: Statement
Reason
lesson 2.5 Geometry.notebook
October 16, 2015
Example 2: Problem­Solving Application
c
lesson 2.5 Geometry.notebook
October 16, 2015
Solve the formula for C. Then find the temerature in degrees Celsius C when it is
Justify each step:
Statement
Reason
Given
lesson 2.5 Geometry.notebook
October 16, 2015
Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry.
C
AC + CB = AB
lesson 2.5 Geometry.notebook
October 16, 2015
Example 3: Solving an Equation in Geometry
Given:
Prove: MO = 6
Reasons
Statements
1)
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
lesson 2.5 Geometry.notebook
Your Turn!
October 16, 2015
Write a justification for each step.
Statements
Reasons
1) Angle Addition Postulate
Substitution Prop (=)
2) 3) Simplify Subtraction Prop (=)
4) 5) Multiplication Prop (=)
lesson 2.5 Geometry.notebook
October 16, 2015
You learned in Chapter 1 that segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.
lesson 2.5 Geometry.notebook
2­5 Algebraic Proof
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
Example 4: Identifying Property of Equality and Congruence
Identify the property that justifies each statement.
A. ∠QRS ≅ ∠QRS B. m∠1 = m∠2 so m∠2 = m∠1 D. 32° = 32°
lesson 2.5 Geometry.notebook
October 16, 2015
Your Turn!
Identify the property that justifies each statement.
a. DE = GH, so GH = DE.
b. 94° = 94°
c. 0 = a, and a = x. So 0 = x.
d. ∠A ≅ ∠Y, so ∠Y ≅ ∠A
lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
lesson 2.5 Geometry.notebook
October 16, 2015
Homework: Due next class
2.5 Page 107 #10­21, 23, 30­32
lesson 2.5 Geometry.notebook
October 16, 2015