2.5: Algebraic Proof

Target: Review & Identify properties of equality.

2.4 RECAP

A biconditional statement combines a conditional and its _______________.

Write the biconditional statement given the conditional.

Conditional: If a 3D solid is a cube, then it has six square faces.

Biconditional:

Determine whether each conditional statement can be written as a TRUE biconditional statement.

Conditional: If a plane figure has four sides, then it is a quadrilateral.

Conditional: If a = 4 and b = 3, then ab = 12.

2.5 NOTES

Reflexive Property: a = _____

Reflexive Property of Congruence: AB AB

1 1m m

4 ___ ___ ___

Symmetric Property: If a = b, then _____________.

Symmetric Property of Congruence: If A B , then ________________.

If m A m B

Then __________________

If AB CD

Then __________________

If ____________________

Then __________________

Transitive Property: If a = b and b = c then _____________.

Transitive Property of Congruence: If A B , and B C , then ________

If m = n and n = r, then

If 4 5 and ________,

then 4 6

If _________ and

__________, then _______.

Substitution Property: If a = b, then b can be substituted for a in any expression.

If a = b, and b + 2 = 10, then

a + 2 = 10.

If MN = 2 and

MN + 8 = AB,

then _________ = AB

If _____________ and

___________, then

_________.

Identify the property that justifies each statement.

1. QRS QRS ________________________________

2. 1 2m m so 2 1m m ________________________________

3. AB CD and CD EF , so AB EF ________________________________

4. 32o = 32o

________________________________

5. If DE=GH then GH=DE ________________________________

6. If 1 and 2 are comp. and 2 3 ________________________________

then 1 and 3 are comp.

7. 5 = a and a=x, so 5 = x. ________________________________

8. If AB = 5 and AB + 6 = CD,

then 11 = CD. ________________________________