Please respond to the following essay question:
Draw and label 2 parallel lines as line m and line n. Add a transversal to your drawing and label it line p. Label all of the angles formed as #1-8. Use your drawing to respond to the following:
a) Name four pairs of corresponding angles.
b) Name two pairs of alternate interior angles.
c) Name two pairs of same-side interior angles.
d) Name two pairs of alternate exterior angles.
To answer the given essay question, we need to follow the instructions step by step and draw the lines mentioned. Here's how we can proceed:
Step 1: Start by drawing two parallel lines, line m and line n. Make sure they are straight and parallel to each other.
Step 2: Next, draw a transversal line p that intersects both line m and line n. The transversal line should cut across the parallel lines at any angle.
Step 3: Label the angles formed by the intersection of the transversal and the parallel lines from 1 to 8. You can simply number them in order, starting from the top left and going clockwise.
Now, with the drawing ready, we can answer the individual questions:
a) Naming four pairs of corresponding angles:
- Angles 1 and 5 are corresponding angles.
- Angles 2 and 6 are corresponding angles.
- Angles 3 and 7 are corresponding angles.
- Angles 4 and 8 are corresponding angles.
b) Naming two pairs of alternate interior angles:
- Angles 3 and 7 are alternate interior angles.
- Angles 4 and 6 are alternate interior angles.
c) Naming two pairs of same-side interior angles:
- Angles 3 and 5 are same-side interior angles.
- Angles 4 and 8 are same-side interior angles.
d) Naming two pairs of alternate exterior angles:
- Angles 1 and 7 are alternate exterior angles.
- Angles 2 and 8 are alternate exterior angles.
Remember, when answering questions like these, it's important to have a clear diagram or drawing available to reference. You can use the labeled drawing to identify and name the different angles in relation to each other accurately.