Properties of Parallel Lines Objectives:  To identify angles formed by two lines and a transversal  To prove and use properties of parallel lines.

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Presentation transcript:

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 Block O Homework Check [10 min] O Warm Up [10 min] O Properties of Parallel Lines [30 min] O Pair Practice [35 min]

Agenda - F Block O Homework Check [10 min] O Construction Practice [20 min] O Collected and Graded for accuracy. O Properties of Parallel Lines [20 min] O Pair Practice [35 min]

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 #1 Find the measure of each angle. Which theorem or postulate justifies each answer?

Example #2 Find the values of x and y.

Example #3 Find the values of x and y.

Two-Column Proof

Proof Example #1 Proof of Alt. Interior Theorem

Proof Example #2

Tips for Success O 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!

HOMEWORK O Page 118 #1-8, #11-17, #30 O TIP: Redraw the figures and highlight the parallel lines to help you “see” the angle pairs.

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