- Identify angles made by transversals: corresponding, alternate interior, alternate exterior and same-side/consecutive interior angles.
Angles and Transversals
Many geometry problems involve the intersection of three or more lines. Examine the diagram below:
In the diagram, lines and are crossed by line . We have quite a bit of vocabulary to describe this situation:
- Line is called a transversal because it intersects two other lines ( and ). The intersection of line with and forms eight angles as shown.
- The area between lines and is called the interior of the two lines. The area not between lines and is called the exterior.
- Angles and are a linear pair of angles. We say they are adjacent because they are next to each other along a straight line: they share a side and do not overlap.
- There are many linear pairs of angles in this diagram. Some examples are and and , and and .
A ________________________________ is a line that cuts across two or more lines.
The area in between lines and is called the __________________________ of the lines.
The area above line and below line is called the _______________________ of the lines.
The word _______________________________ means “next to.”
A linear _____________________ is a set of two angles that are adjacent to each other along a straight line.
The prefix “trans” means “across.”
A transversal cuts across two or more lines.
Other words that have the prefix “trans” are transport (to carry across) and transmit (to send across).
Can you think of some other words that begin with the prefix “trans”?
What do you remember about linear pairs from Unit 1?
- They are adjacent, which means they are right next to each other and they share a side.
- They are supplementary, which means they add up to .
Supplementary angles sum to ____________________.
and in the diagram are vertical angles. They are nonadjacent angles (angles that are not next to each other) made by the intersection of two lines.
- Other pairs of vertical angles in the diagram on the previous page are and and and and .
Pairs of ________________________________ angles are across from each other at an intersection of two lines.
What do you remember about vertical angles from Unit 1?
Vertical angles get their name because they have the same vertex.
- You learned in Unit 1 that vertical angles are congruent. In other words, vertical angles have the same measure.
Corresponding angles are in the same position relative to both lines crossed by the transversal. is on the upper left corner of the intersection of lines and . is on the upper left corner of the intersection of lines and . So we say that and are corresponding angles.
Corresponding angles are in the ________________________ position at each intersection.
and are _________________________________ angles because they are both in the bottom right corner of their intersections.
The word “corresponding” means “matching” or “similar.”
For example, Mexico City corresponds with Washington, D.C., because they are both the capitals of their countries.
Fill in the blanks with the angle that corresponds to each of the following angles in the diagram above. The first one has been done for you.
1. Angle 1 and angle ______.
2. Angle 8 and angle ______.
3. Angle 2 and angle ______.
4. Angle 5 and angle ______.
and are called alternate interior angles. They are in the interior region of the lines and and are on opposite sides of the transversal.
Alternate __________________________ angles are inside lines and and on opposite sides of line , the transversal.
and are another example of __________________________ interior angles.
- Similarly, and are alternate exterior angles because they are on opposite sides of the transversal, and in the exterior of the region between and .
Alternate exterior angles are on opposite sides of the _____________________________.
and are another example of ____________________ ___________________ angles.
If you alternate between two things, you switch between them.
Do you see how alternate angles switch sides?
One angle is to the right of the transversal and the other angle is to the left of the transversal.
To _______________________________ means “to switch.”
- Finally, and are consecutive interior angles. These are also known as same-side interior angles. They are on the interior of the region between lines and and are on the same side of the transversal. and are also consecutive interior angles.
Consecutive interior angles are the same thing as _______________ - ________________ interior angles.
Look at the picture of the lines being cut by a transversal below. Then, circle the type of angle pair represented by the angles given.
1. and corresponding alternate interior alternate exterior same-side interior
2. and corresponding alternate interior alternate exterior same-side interior
3. and corresponding alternate interior alternate exterior same-side interior
4. and corresponding alternate interior alternate exterior same-side interior