LinesSECTION 5.1ESSENTIAL QUESTION: HOW ARE THE MEASURES OF ANGLES RELATED WHEN PARALLEL LINES ARE CUT BY A TRANSVERSAL?HTTPS://WWW.BRAINPOP.COM/MATH/GEOMETRYANDMEASUREMENT/PARALLELANDPERPENDICULARLINES/

VocabularyWhen two lines intersect in a plane and form right angles they are called __________________________.

Two lines are called _________________ when they are in the same plane and do not intersect.

Graphic OrganizerParallel Lines Perpendicular Lines

Symbols

Define it in your own words

Draw it

Describe a real-world example of it

Key Concept: Transversals and Angles

A line that intersects two or more lines is called a _______________, and eight angles are formed

______________ lie inside the lines. Examples: ___________________

______________ lie outside the lines. Examples: ___________________

Key Concept: Transversals and Angles

__________________ are interior angles that lie on opposite sides of the transversal. When the lines are parallel, their measures are equal. Examples: ________________

__________________ are exterior angles that lie on opposite sides of the transversal. When the lines are parallel, their measures are equal. Examples: ____________________

Key Concept: Transversals and Angles

___________________ are those angles that are in the same position on the two lines in relation to the transversal. When the lines are parallel, their measures are equal. Examples: ______________________

Examples Classify each pair of angles in the figure as alternate interior, alternate exterior, or corresponding.

1. 4 and 8∠ ∠

2. 1 and 7∠ ∠

3. 2 and 6 ∠ ∠

Notes: Find Missing Angle Measures

When two parallel lines are cut by a transversal, special angle relationships exist.

If you know the measure of one of the angles, you can find the measures of all of the angles.

Suppose you know that the measure of angle 1 is equal to 50 degrees. You can use that to find the measures of angles 2, 3, and 4.

m 2 = ∠Because ______________________________

m 3 =∠Because ______________________________

m 4 =∠Because _______________________________

ExamplesIf m 4 = 122°, find each given angle measure. Justify your ∠answer.

1. m 8∠

2. m 5∠

3. m 2∠

4. m 1∠

Essential Question How are the measures of the angles related when parallel lines are cut by a transversal?

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