Transcript Math 2 Geometry Based on Elementary Geometry

Math 2 Geometry
Based on Elementary Geometry, 3rd ed, by Alexander & Koeberlein
1.2
Informal Geometry and
Measurement
Vocabulary
“Undefined” terms
• Point: Location but no size. Represented
by a dot. Usually named using upper case
letter. No dimension
• Line: Has infinite length but no width. Has
the quality of “straightness”. Named with
lower case script letter or by identifying two
points contained in the line with double arrow
above. One-dimensional.
• Plane: Has infinite length and infinite width
but no thickness. We use upper case letters to
name planes. Two-dimensional.
Vocabulary
Informal definitions
• A line segment is the portion of a line
between two points. We name the
segment using these two endpoints,
showing a bar above the letters. No bar
refers to the distance between the
endpoints or the length of the segment. If
we use a ruler to measure, we are only
getting an approximation.
Vocabulary
Informal definitions
• Three points are said to be collinear if
they are on the same line. A-X-B will
indicate points A, X, and B are collinear
and X is between A and B.
• If B is a point on the segment AC, then B
is a midpoint of segment AC if AB = BC.
• Two figures of the same shape and size
are said to be congruent. 
Vocabulary
Informal definitions
• An angle has two sides and a common
point called the vertex. The angle can be
named using the vertex only, or using
points from one of each of the sides and
the vertex – in that case the vertex is
always written as the middle point. We
measure angles using a protractor. The
units are degrees. Always use .
Vocabulary
Informal definitions
• If ÐABD is separated into two congruent
angles ÐABC and ÐCBD then ÐABD has
been bisected.
• Any angle measuring 180 is a straight
angle.
• When a straight angle is bisected, the two
angles formed are right angles.
Vocabulary
Informal definitions
• Figures such as triangles and rectangles
are named by listing their vertices.
Adjacent vertices in the name imply that
the line segment containing them are
sides on the figure.
• ABC
• rectangle WXYZ
Vocabulary
Informal definitions
• A circle is the set of all points in a plane
that are a given distance from a given
point (called the center).
• Any line segment joining the center to a
point on the circle is called the radius.
(Plural radii)
• A part of a circle between any two of its
points is called an arc.
Construction:
Bisect a line segment
Given:
Construct:
Segment AB
M so that AM = MB
(M is the midpoint of segment AB)
Construction 2, p. 15 in text