How to identify pairs of lines and special

How to identify pairs of lines and special angles formed by two lines and a transversal? Warm- Up Draw and define each (know slope of parallel and perpendicular lines). Parallel Lines- Perpendicular Lines- Skew Lines-

How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel lines have the _____ slope. Perpendicular lines form _______ angles. Skew lines do not ____ and are not in the _____. * Draw a rectangular prism* Steps: Draw two figures to represent the top and bottom of the prism. Draw the vertical edges. Make the hidden edges of the prism dashed. Label the vertices of the prism. Draw a rectangular prism Complete the following questions Lines p. 146 D G A K E F B C

How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel Lines Cut By a Transversal

How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel Lines Never intersect Equal distance apart; equidistant Symbol || Have the same slope

How to identify pairs of lines and special angles formed by two lines and a transversal? Perpendicular Lines Form 4 right angles Have opposite reciprocal slopes Symbol|

How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel Lines Cut by a Transversal When parallel lines are given in a figure, there are two main areas: the interior and the exterior.

How to identify pairs of lines and special angles formed by two lines and a transversal? A line that intersect two or more lines Form special angles 8 angles are formed when parallel lines are cut by a transversal Transversal

How to identify pairs of lines and special angles formed by two lines and a transversal? Think About It Exterior Interior Exterior

How to identify pairs of lines and special angles formed by two lines and a transversal? Alternate Interior Angles Two angles that lie between the two lines on opposite sides of the transversal Angle measures are CONGRUENT Alternate: opposite Interior: inside

How to identify pairs of lines and special angles formed by two lines and a transversal? Alternate Exterior Angles Two angles that lie outside the two lines on opposite sides of the transversal Angle measures are CONGRUENT Alternate: opposite Exterior: outside

How to identify pairs of lines and special angles formed by two lines and a transversal? Corresponding Angles Two angles that occupy corresponding position Angle measures are CONGRUENT Corresponding: same

How to identify pairs of lines and special angles formed by two lines and a transversal? Vertical Angles formed by intersecting lines Angle measures are CONGRUENT

How to identify pairs of lines and special angles formed by two lines and a transversal? LINEar Pair Two adjacent angles that form a line Angles measures are SUPPLEMENTARY 180 degrees

How to identify pairs of lines and special angles formed by two lines and a transversal? Consecutive Interior Angles AKA: Same-side interior angles Two angles that lie between the two lines on the same side of the transversal Angles measures are SUPPLEMENTARY 180 degrees

How to identify pairs of lines and special angles formed by two lines and a transversal? Summarize What does it mean if two parallel lines are cut by a transversal? Answer: The above six pairs of special angles are formed; angles that are congruent and/ or supplementary

How to identify pairs of lines and special angles formed by two lines and a transversal? Practice p. 148 • Think and Discuss • # 1 - 13

Warm-Up Part 1: Name two pairs of each angles Alternate Interior Alternate Exterior Corresponding Consecutive Interior

Warm-Up Part 2: Identify types of lines and planes Two pairs of parallel segments Two pairs of perpendicular segments A pair of skew segments A pairs of parallel planes

Check Practice 3. 1 Objective: • Identify parallel, perpendicular, and skew lines • Identify the angles formed by two lines and a transversal P. 148 • # 1 - 13 • Think and Discuss

Practice Review Vocabulary

Transversal

Alternate

Interior

Exterior

Corresponding

Consecutive

Vertical

Practice Determine if the pair of angles are CONGRUENT or SUPPLEMENTARY Explain.

Move to the… Left Middle Right Supplementary BOTH Congruent

Red Dots

Orange circles

Parallel Lines Project Objective: • Students will demonstrate their knowledge of parallel lines with a transversal. • Students will show when angles are congruent or supplementary given parallel lines and a transversal Materials: Pencil Colored pencils or markers Ruler Paper (graph paper, if desired) Overview: • For this project, each student will make his or her own street map for a fictional city.

Warm-Up: Find the missing measure. If the m < 5 = 120, find m < 4. ____ If the m < 3 = 72, find m < 8. ____ If the m < 7 = 91, find m < 1. ____ If the m < 6 = 73, find m < 2. ____

126º Xº

Which measurement is incorrect? Fill in the other measurements.

3. 2 Angles Formed by Parallel Lines and transversal Objective: Prove and use theorems about the angles formed by parallel lines and a transversal.

Question When parallel lines are cut by a transversal, the angle pairs formed are either _______or ______.

Answer: When parallel lines are cut by a transversal, the angle pairs formed are either Congruent or Supplementary

Question If a transversal is perpendicular to two parallel lines all eight angles are _____.

Answer: congruent

3 -2 Angles Formed by Parallel Lines and Transversal Activity Materials: Straightedge, protractor, notebook paper, and worksheet Use a pencil and straightedge to darken two parallel lines on a piece of notebook paper. Use your straightedge to draw transversal t. Label each angle #1 – 8. Use your protractor to measure each angle. Make a conjecture about Corresp. Angles, AIA, CIA, AEA, and Lin Pairs formed by two parallel lines cut by a transversal. What appears to be true about each? Complete chart.

3 -2 Angles Formed by Parallel Lines and Transversal Activity Angle Pairs Corresponding Angles 1. Alternate Interior Angles 1. Consecutive Interior Angles 1. Alternate Exterior Angles 1. Linear Pair 1. 2. 2. 2. Measurement Conjecture (sentence)

Continue Parallel Lines Project Draw you OWN city. MUST have • 6 parallel streets • 2 transversal

Warm-Up: Find the missing measure. If the m < 2 = 135, find m < 4. ____ If the m < 3 = 68, find m < 6. ____ If the m < 8 = 87, find m < 1. ____ If the m < 3 = 72, find m < 5. ____

Angle Scramble Work in Pairs Materials: scissors, glue, construction paper, & calculator Show your work Congruent vs. Supplementary

Practice P. 158 # 1 - 11