3.2 Use Parallel lines and 3.2 Use Parallel lines and TransversalsTransversals

Mr. SaucedoGeometryMilby High School

OBJECTIVE:OBJECTIVE:

We will pair angle theorems to find measurements of angles.

ACTIVITYACTIVITYMaterials:

◦Activity worksheet◦Protractor

Step 1: Measure all the angles created by the transverals in the pictures.

Step 2: Look for patterns.

Step 3: Explain your patterns.

POSTULATE 15:POSTULATE 15:CORRESPONDING ANGLESCORRESPONDING ANGLESIf two parallel lines are cut

by a transversal, then the pairs of corresponding angles are congruent.

THEOREM 3.1:THEOREM 3.1:Alternate Interior Angles Alternate Interior Angles TheoremTheoremIf two parallel lines are cut by a

transversal, then the pairs of alternate interior angles are congruent.

<1 ≈ <2

m<1 = m<2

THEOREM 3.2: THEOREM 3.2: Alternate Exterior Angles Alternate Exterior Angles TheoremTheoremIf two parallel lines are cut by a

transversal, then the pairs of alternate exterior angles are congruent.

<1 ≈ <8

m<1 = m<2

THEOREM 3.3:THEOREM 3.3:Consecutive Interior Angles Consecutive Interior Angles TheoremTheoremIf two parallel lines are cut by a

transversal, then the pairs of consecutive interior angles are supplementary.

m<3 + m<5 = 180

or

m<4 + m<6 = 180

CHECKPOINTCHECKPOINTTRUE OR FALSE?

1.Angles A and H are congruent.2.Angles C and E add up to 180 degrees.3.Angles D and F add up to 180 degrees.4.Angles B and G are congruent.5.Angles A and G add up to 180 degrees.6.Angles D and E add up to 180 degrees.7.Angles D and F are supplementary.

CHECKPOINTCHECKPOINTTrue or False?

1.Angles 4 and 6 are congruent.2.Angles 2 and 5 are congruent.3.Angles 7 and 1 add up to 180

degrees.4.Angles 3 and 8 are congruent.5.Angles 8 and 2 add up to 180

degrees.

GUIDED GUIDED PROBLEMPROBLEM

If m<1 = 30, find theMeasurement of all theOther angles.

1 = 5= 2= 6=3= 7=4= 8=

GUIDED PROBLEMGUIDED PROBLEM

m<f = 115 andm<c = x + 5,Find x.

CHECKPOINTCHECKPOINT

m<d = 135 andm<f = x – 30.

Find x.

INDEPENDENT PRACTICEINDEPENDENT PRACTICE

BIG BOOK: PAGE 157PROBLEMS: 1, 4, 5, 6, 7, 8, 10, 12, 14, 18, 22,

33.

PRE-AP: ADD PROBLEM 28.

HOMEWORK:HOMEWORK:

SECTION 3.2WORKBOOK, PAGE 46 & 47

PROBLEMS: 1-20 all problems.