CHAPTER ONE: TOOLS OF GEOMETRY
WHAT THE RESEARCH SAYS…Students retain what they learn from their own efforts to address challenging problems that arise from situations that resonate with their
own interests. (Steen and Forman, 1995)
Chapter one: The tools of geometry. As we begin the study of Euclidean Geometry, it is essential to recognize that with any new course of study, there are tools that
are necessary for success. In the case of your textbook, Chapter one begins with basic definitions of the building blocks of geometry, formulas that you will use to prove
various theorems such as distance and midpoint, and defined relationships with linear measures and angle measures as well as line and angle relationships. You will
develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning and theorems. You will use construction to
explore attributes of geometric figures and to make conjectures about geometric relationships. You will use one and two dimensional coordinate systems to represent
points, lines, rays, lines segments and figures.
Essential Question to answer: Why are geometry and measurement important in the real world?
Section 1.1 Challenge
Section 1.1 Challenge
LESSON 1.1 NOTES: This document is a word document and is editable. Please complete all sections.
WHAT ARE THE UNDEFINED TERMS IN GEOMETRY AND WHY ARE THEY UNDEFINED? Point, line, and plane. In all areas of math, there are
undefined terms. These are things that we believe and base our other ideas on. For example, in geometry, a point is one of those ideas.
Just like the chicken and egg idea, you need a starting point. Once you have one, you can build on that.
WHY ARE TERMS CONSIDERED DEFINED? If the words can be described using known or accepted(agreed upon intuitive definitions) words,
then they are defined.
VOCABULARY
Undefined term, point,
line, plane, collinear,
coplanar, line segment,
endpoint, ray, opposite
rays, intersection
Give a general real world
example. How is this
objective applicable IN
life?
SKETCH A LINE INTERSECTING A PLANE, BUT THAT DOES
NOT LIE IN THE PLANE.
SKETCH TWO PLANES INTERSECTING IN ONE LINE
COMPARE COLLINEAR POINTS AND COPLANAR POINTS. ARE COLLINEAR POINTS ALSO COPLANAR? ARE COPLANAR POINTS ALSO
COLLINEAR? Collinear points are coplanar, but can be in many planes that meet at the line where the points reside. Coplanar points can be
on the same line, but they do not have to be on the same line.
Complete the content
frame for the vocabulary
words for this section.
This is a word document
so you can type on this.
TERM
DEFINITION/ DIAGRAM
POINT
LINE
PLANE
COLLINEAR POINTS
Lie on the same line.
COPLANAR POINTS
RAY
Lie in the same plane.
ENDPOINT
See diagram below. Points located at the end of a line sement.
LINE SEGMENT
OPPOSITE RAYS
INTERSECTION
Two or more geometric figures intersect if they have one or more points in common.
If two distinct lines intersect, they intersect at a point. If two non-parallel planes intersect, they
intersect at a line.
Why are any two points collinear? Two points will always be collinear because through any two points, you can draw one unique line.
Explain why points and lines may be coplanar even when the plane containing them is not drawn. Just because you cannot see something does not mean that it doesn’t
exist. Can you see air? It exists. Are point A and Line GH coplanar? If you said no, ask me in class to show you why. If you said yes, draw in the plane that contains
them.
Why do two intersecting lines always form a plane? Because it is stated that through any three non-collinear points there is one plane, two intersecting lines must
contain AT LEAST three points and therefore make a plane. I line can be drawn through any two points. So two intersecting lines have one point in common and one
point on each of the other lines.
Explain why three coplanar lines may have zero, one, two or three points of intersection. Support your answer with a sketch only.
Zero points of intersection
One point of intersection
SKETCH THREE POSSIBLE INTERSECTIONS OF A LINE AND A PLANE
Two points of intersection
Three points of intersection