Properties of Parallel Lines

Objectives: To identify angles formed by two lines and a

transversal  To prove and use properties of parallel lines

Agenda-E BlockOHomework Check [10 min]OWarm Up [10 min]OProperties of Parallel Lines [30 min]OPair Practice [35 min]

Agenda - F BlockOHomework Check [10 min]OConstruction Practice [20 min]

OCollected and Graded for accuracy.

OProperties of Parallel Lines [20 min]

OPair Practice [35 min]

Warm Up – Try this PSAT question!

Warm Up –Try this PSAT question!

Identifying Angles O A transversal is a line that intersects two

coplanar lines at two distinct points. O Pairs of the eight angles have special names

as suggested by their positions.

Corresponding Angles Postulate

O If a transversal intersects two parallel lines, then corresponding angles are congruent.

Alternate Interior Angles Theorem

O If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Same-Side Interior Angles Theorem

O If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

Pairs that are congruent

What’s the BIG idea?O When you see two parallel lines and a

transversal, and you know the measure of one angle, you can find the measure of ALL of the angles.

Example #1Find the measure of each angle. Which

theorem or postulate justifies each answer?

Example #2Find the values of x and y.

Example #3

Find the values of x and y.

Two-Column Proof

Proof Example #1Proof of Alt. Interior Theorem

Proof Example #2

Tips for SuccessO Highlight the parallel lines.O Know your angle vocabulary!O Know your angle pairs…

O Alt. Interior, Corresponding, Alt. Exterior, Vertical Angles are CONGRUENT

O Same-side interior angles are SUPPLEMENTARY

O Be on the lookout for vertical angles!

HOMEWORKO Page 118 #1-8, #11-17, #30O TIP: Redraw the figures and highlight

the parallel lines to help you “see” the angle pairs.