i)corresponding angles.
ii) Interior alternate angles.
Answers
Answer:
are equal in measure. If two parallel lines are cut by a transversal, the alternate interior angles are congruent. If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.
Explanation:
Angles are Everywhere
Have you ever looked at a sliced pizza and noticed that the beginning of each pizza slice was the same size? Did you ever take the time to wonder why that was? Or, have you ever examined the lines in a parking lot? While you may have noticed all the lines that form the parking spaces, did you ever think about the angles that were formed?
Well, if you haven't before, I'm sure you're thinking of them now. In every pizza and in every parking lot, there are many different angles and angle relationships. In this lesson, we are going to learn about these relationships, ways to identify the relationships and examine the measures of these angles.
Types of Angles
The first angle relationship that we will discuss is vertical angles. They are defined as a pair of nonadjacent angles formed by only two intersecting lines. They are known as 'Kissing Vs' and always have congruent measures. In the figure below, angles 1 and 3 are vertical, as well as angles 2 and 4.
Vertical angles are known as kissing Vs.
vertical angles
The second relationship is corresponding angles. They are considered to be in the same location at each point of intersection. For example, take a look at angles 1 and 3 below. They are both in the upper left corner. Another pair of corresponding angles is angles 6 and 8, which are both in the lower right corner.
Corresponding angles are at the same location on points of intersection.
corresponding angles
Next we have alternate interior angles. Located between the two intersected lines, these angles are on opposite sides of the transversal. Angles 2 and 7 above, as well as angles 3 and 6 are examples of alternate interior angles.
Similarly, we also have alternate exterior angles that are located outside of the two intersected lines and on opposite sides of the transversal. An example of this relationship would be angles 1 and 8, as well as angles 4 and 5.
The last angle relationship is consecutive interior angles. These angles are located on the same side of the transversal and inside of the two lines. In the diagram above, angles 2 and 3 are consecutive interior angles, and so are angles 6 and 7.
With the exception of vertical angles, all of these relationships can only be formed when two lines are intersected by a transversal.
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