Answers:
- Angle 1 and angle 8 are alternate exterior angles (so are angle 5 and angle 4; but you only need to pick one pair)
- Angle 1 and angle 3 are corresponding angles (there are 3 other possible answers. See the second section below)
- Angle 2 and angle 7 are alternate interior angles (so are angle 3 and angle 6; but you only need to pick one pair)
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Explanations:
For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.
When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are
angle 1, angle 5, angle 4, angle 8
The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.
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Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.
Angle 1 and angle 3 are corresponding angles because they
- a) are to the left of each parallel line (m and n)
- b) both below the transversal line
So in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs
- angle 1 and angle 3
- angle 2 and angle 4
- angle 5 and angle 7
- angle 6 and angle 8
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As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.
So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.
