2-5 Algebraic Proof
Warm Up - Solve each equation.
1. 4t – 7 = 8t + 3
2. 2(y – 5) – 20 = 0
3.
Objectives
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
Review properties of equality and use them to write algebraic proofs.
Identify properties of equality and congruence.
Define PROOF:
*The Distributive Property states that a(b + c) =_______________*
Example 1: Solving an Equation in Algebra
Solve the equation & Write a justification for each step.
 4m – 8 = –12

Example 2: Problem-Solving Application
What is the temperature in degrees Fahrenheit F when it is 15°C? Solve the equation
F = 9/5 C + 32 for F and justify each step.
Example 3: Write a Justification for each step.
Numbers are equal (=) and figures are congruent ().
Identify the property that justifies each statement.
A. QRS  QRS
B. m1 = m2 so m2 = m1
C. AB  CD and CD  EF, so AB  EF.
D. 32° = 32°
2-6 Geometric Proof
Objectives


Write two-column proofs.
Prove geometric theorems by using deductive reasoning.
When writing a proof, it is important to justify each logical step with a reason. You can
use symbols and abbreviations, but they must be clear enough so that anyone who reads
your proof will understand them.
Example 1: Write a justification for each step, given that A and B are supplementary and mA = 45°.
1. A and B are supplementary.
mA = 45°
2. mA + mB = 180°
3. 45° + mB = 180°
4. mB = 135°
Write a justification for each step, given that B is the midpoint of AC and AB  EF.
1.
2.
3.
4.
B is the midpoint of AC.
AB  BC
AB  EF
BC  EF
Define Theorem
A geometric proof begins with Given and Prove statements, which restate the hypothesis and conclusion of
the conjecture. In a two-column proof, you list the steps of the proof in the left column. You write the
matching reason for each step in the right column.
Fill in the blanks to complete the two-column proof.
Given: XY
Prove: XY  XY
Statements
Reasons
1.
1.
2.
2.
3.
3.
Fill in the blanks to complete a two-column proof of one case of the Congruent Supplements Theorem.
Given: 1 and 2 are supplementary, and
2 and 3 are supplementary.
Prove: 1  3
Proof:
Use the given plan to write a two-column proof.
Given: 1 and 2 are supplementary, and
1  3
Prove: 3 and 2 are supplementary.
Statements
Reasons
Use the given plan to write a two-column proof if one case of Congruent Complements Theorem.
Given: 1 and 2 are complementary, and
2 and 3 are complementary.
Prove: 1  3
Statements
Reasons
2-7 Flowchart & Paragraph Proof
Use the given flowchart proof to write a two-column proof.
Given: 2 and 3 are comp.
1  3
Prove: 2 and 1 are comp.
Flowchart proof:
Statements
Reasons
Use the given flowchart proof to write a two-column proof.
Given: RS = UV, ST = TU
Prove: RT  TV
Flowchart proof:
Statements
Use the given two-column proof to write a flowchart proof.
Given: B is the midpoint of AC.
Prove: 2AB = AC
Given: 2  4
Prove: m1  m3
Two-column Proof:
Reasons
Use the given paragraph proof to write a two-column
proof.
Given: m1 + m2 = m4
Prove: m3 + m1 + m2 = 180°
Paragraph Proof: It is given that m1 + m2 = m4. 3 and 4 are
supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By
Substitution, m3 + m1 + m2 = 180°.
Statements
Reasons