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Lesson 125: Alternate Interior, Corresponding, and Adjacent Angles
In this lesson we'll do some more geometry work with parallel lines and transversals. Make sure that you understand the previous lesson before starting.
This lesson has some more definitions and concepts that need to be memorized. Very often a test question is designed to simply see if you understand what a term means.
Let's
take a look once again at our parallel lines and transversal.
Look at angles C and F. We define these angles as
alternate interior. They are inside the two parallel
lines, and are on opposite sides of the transversal. D and E
are also alternate interior angles, and notice that alternate
interior angles are equal in measure. C and F happen to be
acute, and D and E happen to be obtuse, but a pair of alternate
interior angles are always equal. Knowing this, we can easily
solve algebra problems involving such angles.
We define angles A and H as alternate exterior angles. They are on the outside of the parallel lines, and are on opposite sides of the transversal. B and G are another such pair. Alternate exterior angles are equal in measure.
We define angles A and E as corresponding angles. They are in corresponding positions. Both are above a parallel line, and both are to the left of the transversal. Corresponding angles are always equal in measure. Angles D and H are also corresponding angles. See if you can find the other two pairs of corresponding angles.
We define angles A and B as adjacent angles, because they share a side in common. Adjacent angles in an arrangement like this are always supplementary, because they lie along a straight line. Angles F and H are also adjacent angles, and therefore supplementary, although they happen to lie along the transversal, and not along one of the parallel lines.
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