Download Lesson 1: Polygons, Triangles, Transversals and Proportional

Lesson 1:
Polygons, Triangles,
Transversals and
Proportional
Segments
Definitions often change. The
definition of a polygon is a good
example. The word is formed from
the Greek roots poly, which means
“more than one” or “many”, and
gonon, which means “angle”. Thus,
polygon literally means “more than
one angle.”
Some figures have and indentation
that we can think of as a cave, and
these polygons are called concave.
Any polygon that does not have a
cave is a convex polygon.
Any two points in the interior of a
convex polygon can be connected
with a line segment that does not
cut a side of the polygon.
Notice that in each figure the
number of vertices (corners) is the
same as the number of sides.
Some polygons of more than 12 sides
have special names, but these names are
not used often. Instead, we use the word
polygon and tell the number of sides or
use the number of sides with the suffix –
gon. Thus, if a polygon has 143 sides, we
would call it “a polygon with 143 sides”
or “143-gon.” The endpoints of one side
of a polygon are called consecutive
vertices, and two adjacent sides are
called consecutive sides. A diagonal of a
polygon is a line segment that connects
two nonconsecutive vertices.
The sum of the measures of the
three angles of any triangle is 180°.
The greatest angle is opposite the
longest side, and the smallest angle
is opposite the shortest side.
Example:
What is the longest side of the
triangle and why?
Answer:
Side c
If two sides of a triangle have equal
lengths, the angles opposite these
sides have equal measures. If two
angles of a triangle have equal
measures, the sides opposite these
angles have equal lengths.
When the three sides of a triangle
have equal lengths, all three angles
are 60° angles. If the three angles
of a triangle are equal, they must
be 60° angles and the three sides
must have equal lengths.
Example:
Find x and y.
X
Y
Answer:
X = 70°
Y = 70°
A transversal is a line that cuts or
intersects two or more other lines.
If a transversal intersects two or
more lines that are parallel and if
the transversal is perpendicular to
one of the parallel lines, it is
perpendicular to all the parallel
lines.
Example: Find the measures of
angles 2, 7 and 8.
Answer:
<2 = 127°
<7 = 127°
<8 = 53°
When three or more parallel lines are
cut by two transversals, the lengths of
the corresponding segments of the
transversals are proportional. This
means that the lengths of the
segments of one transversal are
related to the lengths of the
corresponding segments of the other
transversal by a number called the
scale factor.
Example:
The arrowheads indicate that the
lines are parallel. Find x.
Answer:
x=9
HW: Lesson 1 #1-30