Geometry Flashcards
A point
has no size and is the simplest geometric figure.
All geometric figures consist of
points
A line
is understood to be a straight line that extends in both directions without end.
A plane
can be thought of as a floor or a tabletop, except that a plane extends in all directions without end and has no thickness.
Given any two points on a line, a line segment is
the part of the line that contains the two points and all the points between them.
Given any two points on a line, a line segment is the part of the line that contains the two points and all the points between them. The two points are called
endpoints
congruent line segments
Line segments that have equal lengths
midpoint
The point that divides a line segment into two congruent line segments
line segments BC and CD are
congruent
point c is
halfway between B and D, point C is the midpoint of line segment BD.
Sometimes the notation AB denotes line segment AB, and sometimes it denotes the
length of line segment AB
When two lines intersect at a point, they form
four angles
When two lines intersect at a point, they form four angles. Each angle has
a vertex at the point of intersection of the two lines.
APC and BPD, are called
opposite angles, also known as vertical angles
Opposite angles have
equal measures
congruent angles
angles that have equal measures
Sometimes the angle symbol is used instead of the word
angle
perpendicular lines
Two lines that intersect to form four congruent angles
Two lines that intersect to form four congruent angles are called perpendicular lines. Each of the four angles has a measure of
90º
An angle with a measure of 90º is called a
right angle
this means
perpendicular
acute angle
An angle with measure less than 90º
obtuse angle
an angle with measure between 90º and 180º
parallel lines
Two lines in the same plane that do not intersect
parallel
when two parallel lines are intersected by a third line it formes …… angle/s
8
Label the angles of two parallel lines intersected by a third line
x+y=
180
polygon
a closed figure formed by three or more line segments
sides
line segments
vertices
A polygon is a closed figure formed by three or more line segments, called sides. Each side is joined to two other sides at its endpoints, and the endpoints
convex polygon means
polygon
the term “polygon” means “convex polygon”, that is, a polygon in which
the measure of each interior angle is less than 180°
Triangle (3 sides)
Quadrilateral (4 sides)
Pentagon (5 sides)
all of these are
convex
The simplest polygon is
triangle
quadrilateral can be divided into
2 triangles by drawing a diagonal
a pentagon can be divided
into 3 triangles by selecting one of the vertices and drawing 2 line segments connecting that vertex to the two nonadjacent vertices
If a polygon has n sides, it can be divided into
n-2 triangles
Since the sum of the measures of the interior angles of a triangle is
180 degrees
If a polygon has n sides, it can be divided into (n-2) n minus 2 triangles. Since the sum of the measures of the interior angles of a triangle is 180º, it follows that the sum of the measures of the interior angles of an n sided polygon is
since a quadrilateral has …… sides, the sum of the measures of the interior angles for a quadrilateral is
4
since a hexagon has ………. sides, the sum of the measures of the interior angles for a hexagon is
6
regular polygon means
A polygon in which all sides are congruent and all interior angles are congruent
since an octagon has ……sides, the sum of the measures of the interior angles of an octagon is
8
in a regular octagon the measure of each angle is
The perimeter of a polygon is
the sum of the lengths of its sides
The area of a polygon refers to
the area of the region enclosed by the polygon
Every triangle has
three sides and three interior angles.
Every triangle has three sides and three interior angles. The measures of the interior angles add up to
180°
Every triangle has three sides and three interior angles. The measures of the interior angles add up to 180°. The length of each side must be
be less than the sum of the lengths of the other two sides.
The length of each side must be less than the sum of the lengths of the other two sides. For example,
the sides of a triangle could not have the lengths 4, 7, and 12 because 12 is greater than 4 + 7.
equilateral triangle
A triangle with three congruent sides.
The measures of the three interior angles of such a triangle are also equal, and each measure is 60º.
isosceles triangle
A triangle with at least two congruent sides
