• 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.

    • Upon successful completion of this unit, you will be able to:

      • identify angles, rays, line segments, and points;
      • determine the distance between two points;
      • determine the lengths of a sections of a line segment;
      • measure and classify angles;
      • determine the measurement of unknown angles; and
      • classify polygons by sides.

    • 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.

      • The Distance between Two Points URL

        Read this article and watch the videos. Pay attention to the sections on the ruler postulate and the segment addition postulate. These two postulates help us perform certain measurements. The videos give examples. Read the examples near the end of the page closely to see step-by-step solutions.

        Then, complete review questions 1, 2, 6, 7, 9, 10, 11, 16, and 17 and check your answers.

    • 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.

      • Midpoints and Segment Bisectors URL

        Read this article and watch the video to learn about these concepts. Pay close attention to the midpoint formula, since we use this formula to determine the midpoint of a segment.

        Then, complete guided practice questions 1–3 and check your answers.

    • 1.4: Measuring Angles

      Now that we have studied lines and line segments, we learn about angles between lines or line segments.

      • Angles Page

        First, watch this video to learn the vocabulary of angles.

      • Measuring Angles Page

        Once you feel comfortable with the vocabulary we use to describe angles, watch these videos to learn how to use a protractor, the tool we use to measure angles accurately. The videos also explain the units we use to define angles.

    • 1.5: Congruent Angles and Angle Bisectors

      In this section, we explore how to identify congruent angles and apply properties of an angle bisector.

      • Congruent Angles and Angle Bisectors URL

        Read this article and watch the videos. Pay attention to the section on investigation, which explains the step-by-step method for constructing an angle bisector. Carefully read the examples.

        Then, complete practice questions 1, 5, 11, and 12 and check your answers.

    • 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.

      • Linear Pairs URL

        Read this article and watch the videos to learn about linear pairs, adjacent angles, and angles that form a linear pair. Pay attention to the examples of how to measure angles and identify linear pairs.

        Then, complete review questions 6, 7, 12, and 13 and check your answers.

    • 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.

      • Classifying Polygons URL

        Read this article. The table lists the common types of polygons we will encounter in geometry.