G.GCO.8 Angle Relationships
- Author:
- Dan Dale, GeoGebra Materials Team
Use this worksheet to investigate angle relationships formed when two non-parallel lines are cut by a transversal.
1) Corresponding Angles
Corresponding Angles - the angles which occupy the same relative position at each intersection where a straight line crosses two others.
In this diagram:
AEG and CFG are corresponding (green angles)
AEH and CFH are corresponding (orange angles)
BEG and DFE are corresponding (purple angles)
BEF and DFH are corresponding (blue angles)
2) Alternate Interior Angles
Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
AEF and DFE are alternate interior angles
BEF and CFE are alternate interior angles
3) Alternate Exterior Angles
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
GEA and HFD are Alternate Exterior Angles
BEG and HFC are Alternate Exterior Angles
4) Consecutive Interior (Same-Side Interior) Angles
Consecutive interior angles are the pairs of angles that are between two lines and on the same side of the line cutting through the two lines.
AEF and CFE are Consecutive Interior Angles
BEF and DFE are Consecutive Interior Angles
5) Consecutive Exterior Angles (Same-Side Exterior)
Consecutive exterior angles are exterior angles that lie on the same side of the transversal.
AEG and CFH are Consecutive Exterior
GEB and DFH are Consecutive Exterior
Answer these:
If two non-parallel lines are cut by a transversal:
1. Are corresponding angles congruent (have the same measure)?
2. Are alternate interior angles congruent?
3. Are alternate exterior angles congruent?
4. Are vertical angles congruent?
5. Are same-side interior angles supplementary (sum to 180 degrees)?
6. Are same-side exterior angles supplementary?