MATH 106 Lecture Notes - Lecture 6: Bisection, Skew Lines, Parallelogram
1 Oct 2020
School
Department
Course
Professor
Math 106 Spring 2020
Outline of Ideas for Math 106
Intuitive Geometry
Chapter 11: Introducing Geometry
11.1 Basic Notions of Geometry
Point, Line, Plane, Space
Ray, Segment, (Union and Intersection)
Angle
Acute, Obtuse, Reflex, Straight, zero, right angles
Linear Pairs, vertical angles, complementary angles, supplementary angles
Venn Diagrams – Used to explain and compare
Intersecting lines, Parallel lines, Skew lines
Perpendicular lines and Perpendicular Bisector
Simple Closed curves
Circles
Polygons - specifically Triangles and Quadrilaterals
11.2 Curves, Polygons, and Symmetry
Polygons
Triangles (types)
Quadrilaterals(types)
11.3 More about angles
Two Lines
Triangles
Acute Right Obtuse
Triangles
Isosceles
Equilateral
Scalene
Two Lines
Intersecting Non
Intersecting
Perpendicula
rParallel Skew
Parallel lines*
• Corresponding
• Alternate exterior
• Alternate Interior
• Interior on the same side of the
transversal
• Exterior on the same side of the
transversal
Angles in triangles, quadrilaterals and polygons (Interior and Exterior)
11.4 Three dimensional ( In measurement only)
Chapter 12 Congruence and Similarity with Constructions
12.1 Geometric Constructions (Paper folding, Compass, Computer Tools)
Congruent figures
Geometric Construction of Basic Objects (midpoint, perpendicular bisector,
perpendicular)
Congruent Triangles (SSS, SAS)
Lines and Centers of triangles *
Lines
Altitudes,
Perpendicular Bisectors,
Medians
Angle Bisectors
Centers
Orthocenter,
Circumcenter,
Centroid,
Incenter
12.2 Additional Congruence Theorems
Additional Triangle Congruence Theorems (ASA, AAS)
Quadrilateral Theorems (Nice summary in the review section of chapter 12)
Diagonals of parallelograms, rectangles, etc.
In addition to the definitions for the various quadrilaterals, we proved the following
relationships.
Document Summary
Linear pairs, vertical angles, complementary angles, supplementary angles. Venn diagrams used to explain and compare. Parallel lines: corresponding, alternate exterior, alternate interior. Interior on the same side of the transversal: exterior on the same side of the transversal. Angles in triangles, quadrilaterals and polygons (interior and exterior) 12. 1 geometric constructions (paper folding, compass, computer tools) Geometric construction of basic objects (midpoint, perpendicular bisector, perpendicular) In addition to the definitions for the various quadrilaterals, we proved the following relationships. Quadrilateral theorems (nice summary in the review section of chapter 12) Opposite sides of the parallelogram are congruent diagonals are congruent. Rectangle: in addition to the above that are true for any parallelogram. Rhombus: in addition to the above that are true for any parallelogram. One pair of triangles formed by the intersecting diagonals are similar triangles. The midsegment is the side of the triangle and parallel to it. The segments of the centroid are in a ratio of.
