Question

task 1: a. draw two lines intersected by a transversal. label the lines and number the angles formed. b. using a, give one example for each of the following types of angles pairs: corresponding angles alternate exterior angles alternate interior angles consecutive exterior angles consecutive interior angles

Explanation:

Step1: Draw the lines and angles

Draw two parallel lines \(l_1\) and \(l_2\) and a transversal \(t\) intersecting them. Label the lines. The eight - angle formed can be numbered as \(\angle1,\angle2,\angle3,\angle4,\angle5,\angle6,\angle7,\angle8\) in a clock - wise or counter - clockwise order starting from one of the intersection points.

Step2: Identify corresponding angles

Corresponding angles are in the same relative position. For example, if \(\angle1\) is at the top - left of the intersection of \(l_1\) and \(t\), and \(\angle5\) is at the top - left of the intersection of \(l_2\) and \(t\), then \(\angle1\) and \(\angle5\) are corresponding angles.

Step3: Identify alternate exterior angles

Alternate exterior angles are outside the two lines and on opposite sides of the transversal. For example, if \(\angle1\) is outside \(l_1\) and \(l_2\) on one side of \(t\) and \(\angle7\) is outside \(l_1\) and \(l_2\) on the other side of \(t\), then \(\angle1\) and \(\angle7\) are alternate exterior angles.

Step4: Identify alternate interior angles

Alternate interior angles are between the two lines and on opposite sides of the transversal. For example, if \(\angle3\) is between \(l_1\) and \(l_2\) on one side of \(t\) and \(\angle5\) is between \(l_1\) and \(l_2\) on the other side of \(t\), then \(\angle3\) and \(\angle5\) are alternate interior angles.

Step5: Identify consecutive exterior angles

Consecutive exterior angles are outside the two lines and on the same side of the transversal. For example, \(\angle1\) and \(\angle8\) are consecutive exterior angles.

Step6: Identify consecutive interior angles

Consecutive interior angles are between the two lines and on the same side of the transversal. For example, \(\angle3\) and \(\angle6\) are consecutive interior angles.

Answer:

A. (Drawing description above)
B.

• Corresponding angles: \(\angle1\) and \(\angle5\)
• Alternate Exterior Angles: \(\angle1\) and \(\angle7\)
• Alternate Interior Angles: \(\angle3\) and \(\angle5\)
• Consecutive Exterior Angles: \(\angle1\) and \(\angle8\)
• Consecutive Interior Angles: \(\angle3\) and \(\angle6\)