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Ch 1 Summary
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Chapter 1: Introduction to Geometry Summary Sheet
Undefined Terms
General Terms
point An undefined term thought of as a location with no
size or dimension. It is the most basic building block of
geometry. In a two-dimensional coordinate system, a
point’s location is represented by an ordered pair of
numbers (x, y).
line An undefined term thought of as a straight, continuous
arrangement of infinitely many points extending forever
in two directions. A line has length, but no width or
thickness, so it is one-dimensional.
plane An undefined term thought of as a flat surface that
extends infinitely along its edges. A plane has length and
width but no thickness, so it is two-dimensional.
intersect To cut or cross.
bisect To divide into two congruent parts.
counterexample An example that shows a conjecture to be incorrect or a
definition to be inadequate.
adjacent means next to.
adjacent angles Two angles that share a common vertex, share a common
side and have no common interior points.
consecutive (angles, sides, or vertices of a polygon) Two angles that share
a common side, two sides that share a common vertex, or two vertices
that are the endpoints of one side.
Related Terms
collinear On the same line.
coplanar In the same plane.
Symmetry
symmetry The property that a figure coincides with itself under a
transformation that preserves size and shape.
reflectional symmetry The property that a figure coincides with itself under
a reflection. Also called line symmetry or mirror symmetry.
line of symmetry The line of reflection of a figure having reflectional
symmetry.
bilateral symmetry Reflectional symmetry with only one line of symmetry.
rotational symmetry The property that a figure coincides with itself under
some rotation. If the angle of rotation is 360/n degrees for some positive
integer n, the symmetry is called n-fold rotational symmetry.
Ch 1 Summary
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Lines and Parts of Lines
Angles
line segment Two points and all the points between them
that are collinear with the two points. Also called a
segment. The measure of a line segment is its length.
endpoint The point at either end of a segment or arc, or
the first point of a ray.
midpoint The point on a line segment that is the same
distance from both endpoints. The midpoint bisects the
segment.
ray A point on a line, and all the points of the line that lie
on one side of this point.
angle Two noncollinear rays having a common endpoint.
vertex (of an angle) The common endpoint of the two rays of the angle.
side (of an angle) One of the two rays that form an angle.
measure of an angle The smallest amount of rotation about the vertex
from one ray to the other, measured in degrees.
degree A unit of measure for angles and arcs. 360 of a rotation around a
circle. (protractor A tool used to measure the size of an angle in
degrees.)
congruent segments Two or more segments that have the
same measure or length.
Types of Lines:
perpendicular Lines are perpendicular if they meet at 90°
angles. Line segments and rays are perpendicular if they lie
on perpendicular lines.
parallel Lines are parallel if they lie in the same plane and
do not intersect. Line segments or rays are parallel if they
lie on parallel lines.
skew lines Lines that are not in the same plane and do not
intersect.
congruent angles Two or more angles that have the same measure.
angle bisector A ray that has its endpoint at the vertex of the angle and
that divides the angle into two congruent angles.
adjacent angles Two non-overlapping angles with a common vertex and
one common side.
Types of Angles:
Types of Pairs of Angles:
right angle An angle whose
measure is 90°.
acute angle An angle whose
measure is less than 90°.
obtuse angle An angle whose
measure is greater than 90°,
but less than 180°.
complementary angles Two angles
whose measures have the sum 90°.
supplementary angles Two angles
whose measures have the sum 180°.
vertical angles Two nonadjacent angles
formed by two intersecting lines.
linear pair (of angles) Two adjacent
angles formed by a line and a ray.
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Types of Triangles:
Classified by angle:
right triangle A triangle with a right angle.
acute triangle A triangle with three acute
angles.
obtuse triangle A triangle with an obtuse
angle.
Classified by side:
scalene triangle A triangle with three sides of
different lengths.
equilateral triangle A triangle whose sides
are congruent.
isosceles triangle A triangle with at least two
congruent sides.
Polygons:
Isosceles Triangle Special
Vocab.
vertex angle (of an isosceles
triangle) The angle between the
two congruent sides.
leg The congruent sides.
base (of an isosceles triangle)
The side opposite the vertex
angle.
base angles (of an isosceles
triangle) The two angles
opposite the two congruent
sides.
Types of Quadrilaterals:
trapezoid A quadrilateral with exactly one
pair of parallel sides.
kite A quadrilateral with exactly two distinct
pairs of congruent consecutive sides.
parallelogram A quadrilateral in which both
pairs of opposite sides are parallel.
rhombus An equilateral parallelogram.
rectangle An equiangular parallelogram.
square An equiangular rhombus; equivalently,
an equilateral rectangle.
Names of polygons
Sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
11
Undecagon
12
Dodecagon
n
n-gon
polygon A closed figure in a plane, formed by connecting
line segments endpoint to endpoint with each segment
intersecting exactly two others.
side (of a polygon) A line segment connecting
consecutive vertices of a polygon.
vertex (of a polygon) An endpoint where two sides of
the polygon meet.
angle (of a polygon) An angle having two adjacent
sides of the polygon as its sides.
diagonal A line segment connecting two
nonconsecutive vertices of a polygon or polyhedron.
convex polygon A polygon with no diagonal outside the
polygon.
concave polygon A polygon with at least one diagonal
outside the polygon.
congruent polygons Two or more polygons with the
exact same size and shape.
equilateral polygon A polygon whose sides are
congruent.
equiangular polygon A polygon whose angles are
congruent.
regular polygon A polygon that is both equilateral and
equiangular.
perimeter The length of the boundary of a twodimensional figure. For a polygon, the perimeter is the
sum of the lengths of its sides.
Ch 1 Summary
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Circles:
3-D Figures:
circle The set of all points in a plane at a given distance from a given
point.
center (of a circle) The coplanar point from which all points of the
circle are the same distance.
space An undefined term thought of as the set of all
points. Space extends infinitely in all directions, so it is
three-dimensional.
solid A three-dimensional geometric figure that
completely encloses a region of space.
isometric drawing A drawing of a three-dimensional
object that shows three faces in one view. Also called
an edge view.
net A two-dimensional pattern that can be folded to form
a three-dimensional figure.
solid of revolution A solid formed by rotating a twodimensional figure about a line.
section The intersection of a solid and a plane.
radius A line segment from the center of a circle or sphere to a point on
the circle or sphere. Also, the length of that line segment.
diameter A chord of a circle that contains the center, or the length of
that chord.
chord A line segment whose endpoints lie on a circle.
tangent line A line that lies in the plane of a circle and that intersects the
circle at exactly one point.
point of tangency The point of intersection of a tangent line and a circle.
Types of Solids:
congruent circles Two or more circles with the same radius.
concentric circles Circles that share the same center.
arc Two points on a circle and the continuous part of the circle between
them.
semicircle An arc of a circle whose endpoints are the endpoints of a
diameter.
minor arc An arc of a circle that is less than a semicircle.
major arc An arc of a circle that is greater than a semicircle.
arc measure The measure of the central angle that intercepts an arc,
measured in degrees.
central angle An angle whose vertex is the center of a circle and whose
sides pass through the endpoints of an arc.
Prism
Pyramid
Cylinder
Cone
Sphere
Hemisphere