This Geometry video tutor series consists of 4 tapes containing 16 video segments. Each segment is approximately 25-30 minutes in length. Topics include postulates, proof, triangles, congruence and similarity, parallel lines, quadrilaterals, right triangles, circles, area, coordinate geometry, solids, constructions and introduction to Non-Euclidean geometries.
Video 1 - Postulates & Basic Terms, Proofs, Triangles
This segment covers basic postulates and terms of Euclidean geometry including between, line segment, ray, angle, straight angle, vertical angles, linear pair, and degrees. Also covered are acute, right, and obtuse angles as well as supplementary and complementary angles.
This segment covers the parts of a direct proof and an indirect proof. Theorems are proven by direct proofs using a statement-reason form. "If then" statements are introduced as well as the converse and the contrapositive of these statements.
This segment covers congruent triangles as well as scalene, isosceles, equilateral, right and equiangular triangles. SAS, ASA, and SSS congruencies for triangles are also presented and a few theorems about triangles are proved using direct proofs.
This segment covers exterior angles, concurrent lines, centroid, altitude, and orthocenter. Direct proofs of theorems involving triangles are included.
- Postulates and Basic Terms.
Video 2 -Parallel Lines, Constructions, Quadrilaterals
This segment covers parallel lines, transversals, corresponding angles and alternate interior angles. Euclid's Parallel Postulate is also covered. An example of an indirect proof is included as well as direct proofs. Direct proofs include "The sum of the measures of the angles of a triangle is 180 degrees" and "An exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles."
This segment covers basic geometric constructions with a compass and straightedge. Constructions shown include constructing congruent line segments and angles, bisecting an angle, constructing the perpendicular bisector of a segment, the perpendicular to a line and the medians and altitudes of a triangle
This segment covers convex and concave polygons, regular polygons, the diagonals of a polygon as well as special quadrilaterals including parallelogram, trapezoid, rhombus, rectangle, square and isosceles trapezoid. A direct proof of "The opposite sides and opposite angles in a parallelogram are congruent" is shown.
This segment covers similar polygons and triangles as well as AA, SAS, and SSS similarities for triangles. Exercises are included placing emphasis on the understanding of proportional sides of similar triangles. Direct proofs involving similar triangles are also included.
Video 3 -Right Triangles, Circles, Constructions
This segment covers right triangles, the hypotenuse and the legs of a right triangle, HL congruency theorem, geometric mean, the Pythagorean theorem and 30-60-90 degree and 45-45-90 degree triangles as well as the relationships that exist between the sides of these special triangles. A proof of "The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original right triangle" is included.
This segment covers circles, center, radius, secant, chord, diameter, concentric circles, tangent, point of tangency, semicircle, central angles, minor and major arcs and how they are measured. Direct and indirect proofs are included.
This segment covers inscribed angles and secant angles and their measure. Also covered are the relationships of the lengths of the sides of two chords intersecting in a circle, two secant segments drawn from an external point, and an intersecting tangent segment and secant segment. An example of a direct proof is also included as well as exercises.
This segment covers geometric constructions with a compass and a straightedge. Constructions shown include dividing a line segment into a given number of congruent segments, constructing the fourth proportional to three given segments, constructing a circle given three points that are not colinear, constructing the tangent to a circle from a point on the circle, constructing the tangents to a circle from an external point, and constructing an equilateral triangle given a side.
Video 4 -Area, Solids, Coordinate Geometry
This segment includes the concepts of perimeter and area. Circumference of a circle is presented as well as area formulas of a rectangle, triangle, parallelogram, circle, trapezoid, and square. Exercises finding perimeters and areas are also included.
This segment covers the Cartesian or rectangular coordinate system as well as the midpoint formula and the distance formula. Slope is covered as well as parallel lines, perpendicular lines, and slope-intercept and point-slope forms of lines. The standard form of a circle is also included.
This segment covers convex solids and polyhedrons as well as face, vertex, and side of a polyhedron. Regular polyhedrons, prisms, parallelepipeds, pyramids, sphere, cones and cylinders are also included. The concept of surface area and volume is covered as well as formulas for some convex solids.
This segment covers a comparison of Euclid's Parallel Postulate to the Riemann Postulate and the Gauss-Lobachevski-Bolyai Postulate. Interesting facts about Elliptic geometry are presented by looking at a spherical model. Also some properties of Hyperbolic geometry are covered.
- Introduction to Non-Euclidean Geometry.