Download Section 1-6.notebook

Section 1­6.notebook
September 05, 2014
Math 2 ~ Naylor
Section 1­6: Reasoning in Algebra and Geometry
I CAN prepare to prove theorems about triangles.
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 ac = bc
Division Property: If a = b, 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
Distributive Property: a(b ± c) = ab ± ac
Proof: a convincing argument that uses deductive reasoning
Two­Column Proof: lists each statement on the left and the justification on the right
Section 1­6.notebook
September 05, 2014
Justifying Steps When Solving an Equation
Example 1: What is the value of x? Justify each step.
Example 2:
What is the value of x? Justify each step.
Using Properties of Equality and Congruence
Example 3:
What is the name of the property or congruence that justifies going from the first statement to the second statement?
2x + 9 = 19
2x = 10
Example 4:
What is the name of the property or congruence that justifies going from the first statement to the second statement?
<O ≅ <W and <W ≅ <L
<O ≅ <L
Example 5:
What is the name of the property or congruence that justifies going from the first statement to the second statement?
m<E = m<T
m<T = m<E
Section 1­6.notebook
September 05, 2014
Writing a Two­Column Proof
Example 6:
Write a two­column proof.
Given: m<1 = m<3
Prove: m<AEC = m<DEB
Statements
1)
Reasons
1)
2)
2)
3)
3)
4)
4)
5)
5)
Example 7:
Write a two­column proof.
Given: AB ≅ CD
Prove: AC ≅ BD