Geometry - branch of mathematics that deals with points, lines, planes and solids and examines their properties.
Point – has no
size; length, width, or height. It is
represented by a dot and named by a capital letter.
Line – set of
points which has infinite length but no width or height. A line is named by a lower case letter or by
any two points on the line.
Plane
–
set of points that has infinite length and width but no height. We name a plane
with a capital letter.
Space – set of all
points.
Collinear
points
– points that lie on the same line.
Noncollinear
points
– points that do not lie on the same line.
Coplanar
points
– points that lie on the same plane.
Noncoplanar
points
– points that do not lie on the same plane.
Segment – part of a
line that consists of two points called endpoints and all points between them.
Ray- is the part
of a line that contains an endpoint and all points extending in the other
direction.
Congruent
segments
– segments that have the same length.
Bisector
of a segment
– line, ray segment, or plane that divides a segment into two congruent
segments.
Midpoint
of a segment
– a point that divides the segment into two congruent segments.
Acute
angle
– angle whose measure is between 0 degrees and 90 degrees.
Right
angle
– angle whose measure is 90 degrees.
Obtuse
angle
– angle whose measure is greater than 90 degrees but less than 180 degrees.
Straight
angle
– angle whose measure is 180 degrees.
Congruent
angles
– angles that have the same measure.
Angle
bisector
– ray that divides an angle into two congruent adjacent angles.
Triangle – the figure
formed by three segments joining three noncollinear points. Each of the three
points is a vertex of the triangle and the segments are the sides.
Acute
triangle-
triangle that has all acute angles.
Right
triangle
– triangle with a right angle.
Obtuse
triangle
– triangle with an obtuse angle.
Equiangular
triangle
– triangle with all angles congruent.
Scalene
triangle
– triangle with no sides congruent.
Isosceles
triangle
– triangle with at least two sides congruent.
Equilateral
triangle
– triangle with all sides congruent.
Adjacent
angles
– two coplanar angles with a common vertex and a common side between them
Vertical
angles
– the non-adjacent angles formed by two intersecting lines.
Complementary
angles
– two angles whose sum is 90 degrees.
Supplementary
angles
– two angles whose sum is 180 degrees.
Perpendicular
lines
– two lines that intersect to form right angles.
Parallel
lines
– two lines are parallel if they are coplanar and do not intersect.
Skew
lines
– are noncoplanar lines they will not intersect.
Polygon – union of 3
or more coplanar segments that meet only at endpoints such that at most two
segments meet at one endpoint and each segment meets exactly two other
segments.
Regular
polygon
– polygon which is equilateral and equiangular.
Congruent
triangles
– two triangles are congruent if corresponding sides are congruent and
corresponding angles are congruent.
Median
of a triangle
– segment from the vertex of a triangle to the midpoint of the opposite side.
Altitude
of a triangle
– segment from the vertex of a triangle perpendicular to the line containing
the opposite side.
Parallelogram –
quadrilateral with both pairs of opposite sides parallel.
Rectangle –
parallelogram with a right angle.
Rhombus –
parallelogram with consecutive sides congruent.
Square – all sides
congruent and all four right angles.
Trapezoid –
quadrilateral with exactly one pair of opposite sides parallel.
Ratio
–
comparison of two numbers by division.
Proportion – equation
that states two ratios are equal.
Pythagorean
Theorem
– in a right triangle, the sum of the squares of the legs is equal to the
square of the hypotenuse
Circle – the set of
points in a plane that are equidistant from a fixed point called the center.
Radius – segment
whose endpoints are the center of the circle and a point on the circle.
Chord – segment
that connects two points on the circle.
Diameter – chord that
passes through the center of the circle.
Secant – line that
intersects a circle in two points.
Tangent – line in the
plane of the circle that intersects the circle in one point.
Concentric
circles
– two or more circles in the same plane with the same center.
Congruent
circles
– circles that have congruent radii.
Sphere – set of
points in space a given distance from a given point called the center.
Arc – consists of
two points and the continuous part of a circle between them.
Semi-circle – arc whose
endpoints are the endpoints of a diameter.
Minor
arc
– arc whose measure is less than a semi-circle or 180 degree.
Major
arc
– arc whose measure is greater than a semi-circle or 180 degrees.
Central
angle of a circle
– angle whose vertex is the center of the circle and whose rays are radii of
the circle.
Congruent
arcs
– arcs with equal measure in the same circle or in congruent circles.
Inscribed
angles
– angle whose vertex is on the circle and whose sides are chords of the circle.
Bases – congruent
polygons lying in parallel planes.
Altitude – segment
joining the two base planes and perpendicular to both.
Lateral
faces
– faces of a prism that are not its bases.
Lateral
edges
– intersection of adjacent lateral faces form lateral edges.
Lateral
area
– sum of the area of its lateral faces.
Surface
area
– sum of the area of all its faces.
Volume – number of
cubic units contained in a solid.
Right
Prism – is a prism whose lateral faces are rectangles.
Oblique prism – is a prism
whose lateral faces are parallelograms.
Cube – is a prism
where all sides are squares.
Triangular
prism
– is a prism whose parallel faces (the bases) are congruent triangles.
Cylinder – has two
congruent circular bases in parallel planes.
Cone – has a vertex
and a circular base.
Line of
symmetry
– divides a figure into two congruent halves that reflect each other.
Perimeter – of a polygon
is the distance around the polygon.
Area – of any
surface is the number of square units required to cover the surface.
Volume – of a
3-dimensional figure is the number of cubic units contained in the solid.
Circumference – the
distance around a circle.
Conditional
statement
– a statement that can be written in an if-then form.
Hypothesis – in a
conditional statement the statement that immediately follows the word if.
Conclusion – in a
conditional statement the statement that immediately follows the word then.
Converse – the
statement formed by exchanging the hypothesis and the conclusion of a
conditional statement.
Inverse – the
statement formed by negating both the hypothesis and the conclusion of a
conditional statement.
Contrapositive – the
statement formed by negating both the hypothesis and conclusion of the converse
of a conditional statement.
Biconditional – the
conjunction of a conditional statement and its converse.
Deductive
reasoning
– a system of reasoning that uses facts, rules,definitions, or properties to
reach logical conclusions.
Inductive
reasoning
– reasoning that uses a number of specific examples to arrive at a plausible
prediction.
Proof – a logical
argument in which each statement you make is supported by a statement that is
accepted as true.
Postulate- a statement
that describes a fundamental relationship between basic terms of geometry.
Postulates are accepted as true without proof.
Theorems – a statement
or conjecture that can be proven true by given, definitions, postulates, or
already proven theorems.
Two-column
proof
– a formal proof that contains statements and reasons organized in two columns.
Paragraph
proof
– an informal proof written in the form of a paragraph that explains why a conjecture
for a given situation is true.
Flow proof – a proof
that organizes statements in logical order, starting with given statements.
Each statement is written in a box with the reason verifying the statement
written below the box.
Conjecture – an educated
guess based on known information.
Sine – for an
acute angle of a right triangle, the ratio of the measure of the leg opposite
the acute angle to the measure of the hypotenuse.
Cosine – for an
acute angle of a right triangle, the ratio of the measure of the leg adjacent
to the acute angle to the measure of the hypotenuse.
Tangent – for an
acute angle of a right triangle, the ratio of the measure of the leg opposite
the acute angle to the measure of the leg adjacent to the acute angle.
