Unit 1: The Basics of Geometry
In this unit, we will explore the basic building blocks, vocabulary, and classifications of geometry. If you know how to identify and classify the shapes and properties of certain types of triangles, you can apply the appropriate rules and relationships to quickly and easily make predictive calculations.
Completing this unit should take you approximately 5 hours.
1.1: Language and Notation
In this section, we discuss the vocabulary you need to know to understand geometry. You should be comfortable with the meaning of the words used in geometry so you can use its language to understand and solve geometry problems.
1.2: The Distance between Two Points
Now that we have reviewed the basic language you need to know to understand geometry, we are ready to begin problem solving. First, let's explore how to determine the distance between two points on a line segment.
1.3: Midpoints and Segment Bisectors
A midpoint is the point on a line segment that divides it into two equal parts or the halfway point of a line segment. A segment bisector is a line, ray or segment that cuts another line segment into two equal parts.
1.4: Measuring Angles
Now that we have studied lines and line segments, we learn about angles between lines or line segments.
1.5: Congruent Angles and Angle Bisectors
In this section, we explore how to identify congruent angles and apply properties of an angle bisector.
1.6: Acute, Obtuse, and Right Angles
Acute angles are less than 90 degrees, right angles are 90 degrees, and obtuse angles are greater than 90 degrees.
1.7: Complementary and Supplementary Angles
A set of complementary angles add up to 90 degrees. A set of supplementary angles add up to 180 degrees.
1.8: Linear Pairs
A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. Two angles are adjacent when they have a common side and a common vertex (corner point) and do not overlap.
1.9: Vertical Angles
Vertical angles are nonadjacent angles formed by intersecting lines. We can determine the angles of vertical angles based on what we have already learned in this unit.
1.10: Polygon Classification
Now we can combine line segments with certain angles to form shapes called polygons. In this section, we classify polygons based on the types of angles (concave or convex) used to produce them.