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GEOMETRY NVESTIGATION Corresponding and Alternate Angles Objective: In this investigation you will learn about corresponding angles and alternate angles. PART 1 : Corresponding Angles Step 1: In the space below are two parallel lines. (Trust me on this one.) Draw a transversal through the parallel lines. Step 2: Label the eight angles created “1” through “8” Step 3: There are four pairs of corresponding angles. Label them in the chart below: Angle ______ corresponds to angle _____. Angle ______ corresponds to angle _____. Angle ______ corresponds to angle _____. Angle ______ corresponds to angle _____. Step 4: Choose one pair of corresponding angles to work with. What pair are you using? < and < Measure each angle with a protractor. Write their measurements here: What do you notice? Step 5: Repeat Step 4 with your next pair of corresponding angles. Step 6: Write your conjecture about the measures of corresponding angles below. Conjecture: If two parallel lines are cut by a transversal, then the measures of corresponding angles are _________________________________. PART 2: Alternate Interior Angles Step 1: Using the parallel lines and the numbered angles on the front side. Answer the following Angle ______ is an alternate interior angle with angle _________. Angle ______ is an alternate interior angle with angle _________. Step 2: Measure the first pair of alternate interior angles. What do you notice about the measurement: Step 3: Repeat Step 2, and write a conjecture below: CONJECTURE: If you have two parallel lines cut by a transversal, then the measures of alternate interior angles are _________________________. Part 3: Alternate Exterior Angles Step 1: Using the parallel lines and the numbered angles on the front side. Label the two pairs of alternate exterior angles. Angle ______ is an alternate exterior angle with angle _________. Angle ______ is an alternate exterior angle with angle _________. Step 2: Measure the first pair of alternate exterior angles. What do you notice about the measurement: Step 3: Repeat Step 2, and write a conjecture below: CONJECTURE: If you have two parallel lines cut by a transversal, then the measures of alternate exterior angles are _________________________.