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Intro to Proofs
Unit IC Day 2
Do now

Solve for x
5x – 18 = 3x + 2
Theorems
Recall: A postulate is a rule that is
accepted without ___________
 A theorem is a true statement that
follows from _________________

◦ All theorems must be ______________
Algebraic Properties of Equality
Let a, b, and c be real numbers.

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 and c ≠ 0, then a/c = b/c.
Algebraic Properties of Equality
Let a, b, and c be real numbers.

Reflexive property: a = a.

Symmetric property: If a = b, then b = a.

Transitive property: If a = b and b = c, then a = c.

Substitution property: If a = b, then a can be
substituted for b in any equation or expression.
Example 1

Solve for x. Justify each step.
10
20 = 220 - x
7
They work for geometry, too!
Definition of congruence
Informal: Two geometric figures are
congruent if they have the exact same size
and shape.
 Definition: If two figures are congruent,
then their ______________ are equal.
◦ Must use this to move between “≅” and “=” in
a proof!
Types of Proof
Two-column proof: statements in one
column, reasons in the other
 Paragraph proof: statements and
reasons in paragraph form
 Flow proof: statements and reasons
arranged graphically with arrows showing
direction of logic

Example 2
More Theorems

Note: this is not the definition of a right
angle— measure is 90º
Proof of Theorem 2.3
More Theorems
Example 3
Closure

Draw an example diagram in which
1 and 3 are both linear pairs with
2. Tell two ways you can prove m1
= m3.