- Topics At a Glance
- Basic Shapes & Angles
- Angles
- Parallel Lines & Transversals
- Polygons
- Triangles
- Quadrilaterals
- Angles in a Polygon
- Circles
- Similar Figures
- Perimeter & Circumference
- Area (Polygon, Triangle, Circle, Square)
- Area Formulas
- Area of Irregular Shapes
- 3D Objects (Prisms, Cylinders, Cones, Spheres)
- Volume of Prisms & Cylinders
- Volume of Pyramids & Cones
- Volume of Spheres
- Surface Area
- Pythagorean Theorem
Introduction to Parallel Lines & Transversals:
A transversal is a line that intersects two or more other lines. When it intersects parallel lines, many angles are congruent. Let's take a peek at what this means. Lines k and j are parallel. Line l is a transversal.
As we mentioned before, when this happens we get a bunch of pairs of congruent angles. These pairs have nifty vocabulary terms to go with them. Here they are:
- Corresponding angles - angles that are in the same position on each line. There are four sets of these angles:
. - Alternate interior angles - angles on the opposite sides of the transversal and on the interior of the parallel lines. There are two sets of alternate interior angles:
. - Alternate exterior angles - angles on opposite sides of the transversal and on the exterior of the parallel lines. There are two sets of alternate exterior angles:
.
Look Out: these pairs of angles are congruent only when the transversal cuts parallel lines.
Parallel Lines & Transversals Practice:
Example 1
Lines j and k are parallel.
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.
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Refer to this diagram for Exercises 1-4
Lines m, n, and o are parallel.
Exercise 1
What angles are corresponding to 
?
Exercise 2
What is the measure of 
?
Exercise 3
Which angles have measurements of 75°?
Exercise 4
Which angles have measures of 105°?
