Properties and Parallel Line Theorems (Geo 3.2 day 2)

Geometry 3.2 day 2

The theorems & properties...

Learning Target

I can identify which property or theorem to use in specific situations from CIA, AIA, CAP, VAT, LPT, AEA, reflexive, symmetric and transitive.

FOR THIS LESSON

• You want to get this DOWN

• Matches page 3 in notes

• Take GOOD NOTES!!!

PROPERTIES

REFLEXIVE: a = a

SYMMETRIC: a = b so b = a

TRANSITIVE: a = b & b =c , then a = c

PROPERTIES

REFLEXIVE: something is equal (congruent) to itself

SYMMETRIC: if thing A is equal (congruent) to thing B, then thing B is equal (congruent) to thing A

TRANSITIVE: if thing A is equal (congruent) to thing B and thing B is equal (congruent) to thing C then thing A is equal (congruent) to thing C

Multiple Choice

Which property:

b = b

• Transitive

• Symmetric

• Reflexive

Multiple Choice

Which property:

a = b so b = a

• Transitive

• Symmetric

• Reflexive

Multiple Choice

Which property:

4 $5 bills is $20

2 $10 bills is $20

So, 4 $5 bills is the same as 2 $10 bills

• Transitive

• Symmetric

• Reflexive

Multiple Choice

Which property:

AD = AD

• Transitive

• Symmetric

• Reflexive

If two angles form a linear pair then they are supplementary.

We call this the Linear Pair Theorem.

We abbreviate with LPT.

We will use this as a REASON in proofs.

Linear Pair Theorem (LPT)

Because $\angle4\ and\ \angle2\$ form a linear pair, they are supplementary.

IF two angles are vertical angles, THEN they are congruent.

• We call this the Vertical Angle Theorem.

• We will use this as a REASON in proofs.

Vertical Angle Theorem (VAT)

 $\angle ACB\ \cong\angle ECD$  

IF parallel lines are cut by a transversal, THEN corresponding angles are congruent.

We call this the Corresponding Angles Postulate.

We abbreviate with CA.

We will use this as a REASON in proofs.

Corresponding Angles Postulate (CAP)

 $\angle7\ \cong\ \angle3$  

IF parallel lines are cut by a transversal, THEN alternate interior angles are congruent.

We call this the Alternate Interior Angles Theorem

We abbreviate with AIA

We will use this as a REASON in proofs.

Alternate Interior Angles Theorem (AIA)

 $\angle3\ \cong\ \angle6$  

IF parallel lines are cut by a transversal, THEN alternate exterior angles are congruent.

We call this the Alternate Exterior Angles Theorem

We abbreviate with AEA

We will use this as a REASON in proofs.

Alternate Exterior Angles Theorem (AEA)

 $\angle2\ \cong\ \angle7$  

IF parallel lines are cut by a transversal, THEN consecutive interior angles are congruent.

We call this the Consecutive Interior Angles Theorem

We abbreviate with CIA

We will use this as a REASON in proofs.

Consecutive Interior Angles Theorem (CIA)

 $\angle4\ and\ \angle6\$  are supplementary.
NOT add to 180 degrees!!!!!!!!!

Multiple Choice

What tells us

 $\angle3\ \cong\angle7$  

• VAT

• LPT

• CAP

• CIA

Multiple Choice

What tells us

 $\angle1\ \cong\angle8$  

• VAT

• AEA

• CAP

• CIA

Multiple Choice

What tells us

 $\angle1\ \cong\angle4$  

• VAT

• AEA

• CAP

• CIA

Multiple Choice

What tells us

 $\angle5\ \cong\angle4$  

• LPT

• AEA

• AIA

• CIA