Unit Objective:
You will become proficient at identifying relationships between points, lines and planes including angle measurements and classifications.
Day 1: Back to the Basics
Most of us know what we are talking about when we hear to terms point, line or plane. However, these terms are actually undefined terms but we general agree that they mean the following...
A point has no dimension. It is usually represented by a small dot.
A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions.
A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end, even though the drawing of a plane appears to have edges.
There are a few terms we need to be familiar with for this unit.
The line segment or segment AB consists of the endpoints A and B, and on line AB that are between A and B.
The ray AB consists of the initial point A and all points on line AB that lie on the same side of A as point B.
Day 2, 3, & 4: Angles
An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.
We classify angles according to their angle measure.
The measure of an angle can be approximated with a protractor, using units called degrees (°).
There are four classifications of angles
When talking about angles it may also be helpful to identify points on the interior/exterior of the angle.
A point is in the interior of an angle if it is between points that lie on each side of the angle.
A point is in the exterior of an angle if it is not on the angle or in its interior.
Complimentary angles are two angles whose measures add up to 90°
Supplementary angles are two angles whose measures add up to 180°
Complimentary/Supplementary Angle Activity
Two angles with the same angle measures are called congruent angles.
An angle bisector is a ray that divides an angle into two adjacent angles that are congruent.
Angle Bisector Construction Activity
Days 5, 6 & 7: Parallel lines, Perpendicular lines and Skew lines
Parallel Lines
Perpendicular Lines
Skew Lines
Parallel and Perpendicular Activity using GSP
Days 8, 9 & 10: Two line cut by a transversal
A transversal is a line that intersects two or more coplanar lines at different points.
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
If two parallel lines are cut by a transversal, then the pair of alternate interior angles are congruent.
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
If tow parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
