Introduction to Geometry
A brief overview of the following lessons.
Basics of Geometry
This chapter includes activities that allow students to explore distances, midpoints, and angle pairs in the coordinate plane.
Reasoning and Proof
This chapter tasks students with examining conditional statements in order to derive logical statements through inductive and deductive reasoning.
Parallel and Perpendicular Lines
This chapter explores the properties of angles and slopes formed by parallel and perpendicular lines, especially when cut by transversals.
This chapter focuses on investigating side and angle relationships in congruent triangles as well as making conjectures based on interior and exterior angles. Also covered are the conditions for congruence.
Relationships within Triangles
This chapter utilizes exercises that cover the perpendicular bisector theorem, angle bisector theorem, and the median and centroid of a triangle.
This chapter explores the properties of various quadrilaterals, including parallelograms, trapezoids, rhombi, and kites.
This chapter allows students to investigate various methods of constructing similar triangles including utilizing the side-splitter theorem.
Right Triangle Trigonometry
This chapter tasks students with proving the Pythagorean theorem using the Cabri Jr. application in addition to covering the properties of special triangles such as the 45-45-90, 30-60-90, and isosceles triangles.
This chapter includes exercises which ask students to deduce corollaries for the perpendicular bisector theorem, discover the inscribed angle theorem, and find the chord-chord, secant-secant, and secant-tangent theorems.
Perimeter and Area
This chapter allows students to explore the relationship between a circle’s circumference and its diameter as well as the area of regular polygons in terms of the apothem and the perimeter.
Surface Area and Volume
This chapter explores the net representation of a right cylinder, allowing students to develop the surface area from parts of the net.
This chapter covers transformation concepts such as reflections, rotations, translations, and dilations. Students are also introduced to drawing from both one and two point perspectives.