Foundations of Geometry (8 Block Days)
Conceptual understanding of points, lines and planes are used to connect geometric systems to knowledge of the real world. Finding midpoints, distances, and slope are essential to solving many real-world problems.
Focus TEKS
G.1A Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning and theorems
G.1B Recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes (S)
G.1C Compare and contrast the structures and implications of Euclidean and non-Euclidean geometries. (S)
G.2A Use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships (S)
G.7A Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures (S)
G.7B Uses slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons (R)
G.7C Derive and use formulas involving length, slope and midpoint (R)
G.9A Formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models (S)
Students will know…
the difference between Euclidean and Spherical Geometry
geometric shapes are created by combining the three undefined terms in Euclidean geometry
the names and symbols for the initial geometric shapes in Euclidean geometry
how to determine if a pair of lines are skew, parallel, perpendicular or intersecting in a plane
Students will be able to…
determine the slope, midpoint and length of a line segment on the coordinate system.
solve problems involving slope, midpoint, and length in the coordinate system.
write the equations of a pair of lines that are parallel, perpendicular or intersecting in a plane
write the equations of perpendicular bisectors of a line segment
construct basic Euclidean figures using a compass and straight edge.
Lesson Plan
Regular Geometry
Pre-AP Geometry
8/26-27 Syllabus and Types of Geometry
8/28-29 Points, Lines and Planes
9/2-3 Constructions plus Quiz
9/4-5 Segment and Angle Postulates
9/8-9 Foundations EXAM
9/10-11 Distances and Fractional Distances
9/12 & 15 Equations of Lines
9/16-17 Parallel and Perpendicular Line Equations
9/18-19 Lines and Distances Exam #2
8/26-27 Syllabus and Types of Geometry
8/28-29 Points, Lines, Planes and Constructions
9/2-3 Finish Constructions, Segment and Angle Postulates plus Quiz
9/4-5 Distances and Fractional Distances
9/8-9 Foundations EXAM
9/10-11 Equations of Lines and Parallel/Perpendicular Lines
9/12 & 15 Bridge Project Overview
9/16-17 Bridge Project - Step 1