Download Chapter 4 Vocabulary - Neshaminy School District

VOCABULARY
Chapters 1, 2, 3, 4, 5, 9, and 8
WORD
Acute angle
IMAGE
DEFINITION
An angle with measure between 0° and 90°
56
•
Acute triangle
A triangle with three acute angles.
60
50
70
Adjacent angles
Two angles in a plane that have a common
vertex and a common side but no common
interior points.
∠1 and ∠2 are adjacent angles
Two nonadjacent interior angles on
opposite sides of the transversal.
1 2
Alternate interior
angles
*When 2 parallel lines are cut by a
transversal, alternate interior angles are
congruent.
Altitude of a triangle
Angle
A figure formed by two rays that have the
same endpoint.
•
Angle of Depression
Angle of Elevation
Bi-conditional
Statement
A statement that contains the words “if and
only if.”
Angle bisector
A ray that divides the angle into two
congruent adjacent angles.
⃗⃗⃗⃗⃗⃗ bisects ∠ABC, then ∠1 ≅ ∠2.
If 𝐵𝐷
Centroid
Circumcenter
Collinear points
Complementary
angles
•
30°
Points all in one line.
•
•
Two angles whose measures have a sum of
90°.
60°
Conclusion
A statement whose basic form is If p, then
q. “ q” is the conclusion.
Conditional
Statement
A statement in the form “if –then.” The
basic form of a conditional statement is “If
p, then q.”
Congruent angles
Angles with equal measurement
Congruent polygons
Figures that have the same size and shape.
Congruent segments
Segments that have equal lengths.
Converse
The statement formed by switching the
hypothesis and conclusion of a conditional
statement: If q, then p.
Coplanar points
Points all in one plane.
Corresponding
angles
Two angles in corresponding positions
relative to two lines.
*When 2 parallel lines are cut by a
transversal, corresponding angles are
congruent.
Cosine
Counterexample
Deductive reasoning
Dilation
Ex. If an animal is a bird, then it can fly.
Counterexample: A penguin is a bird, but
cannot fly. Therefore, a “penguin” is a
counterexample.
Solving a proof is an example of using
deductive reasoning.
An example used to prove that an if-then
statement is false.
Proving statements by reasoning from
accepted postulates, definitions, theorems,
and given information.
A transformation that preserves angle
measure and results in an image with
lengths proportional to the pre-image
lengths. Example: Changing a smaller
image into a bigger image.
Equiangular triangle
A triangle with all angles congruent.
Equidistant
The same distance from two or more
objects.
Equilateral triangle
A triangle with three congruent sides.
Exterior angle of a
triangle
ExteriorAngle
The angle formed when one side of the
triangle is extended.
Hypotenuse
The longest side of a right triangle located
across from the right angle.
Hypothesis
A statement whose basic form is If p, then
q. Statement p is the hypothesis.
Image
Each point P in a given set is mapped to
exactly one point P’ in the same or a
different set. P’ is called the image of P.
Incenter
Inductive reasoning
A pop quiz is given the first three Fridays
of the school year, so you conclude their
will be a pop quiz every Friday.
A kind of reasoning in which the conclusion
is based on several past observations.
Isosceles triangle
A triangle with at least two sides congruent.
Legs of an isosceles
triangle
The two congruent sides.
Legs of a right
triangle
The two sides of a triangle that create the
right angle.
Length of a segment
The distance between its endpoints.
Line
A geometric figure which extends in two
directions without ending. It has infinite
points and no thickness.
A pair of adjacent angles whose
noncommon sides are opposite rays.
Linear Pair
Median of a triangle
Midsegment of a
triangle
Midpoint
The point that divides a segment into two
congruent segments.
Non-collinear points
Points not all in one line.
Non-coplanar points
Points not all in one plane.
Obtuse angle
An angle with measure between 90° and
180°.
Obtuse triangle
A triangle with one obtuse angle.
Opposite rays
Rays that have the same endpoint and go in
opposite directions.
Orthocenter
Parallel lines
Coplanar lines that do not intersect.
Parallel planes
Planes that do not intersect.
Perpendicular
bisector of a
segment
A line, segment, ray, or plane that is
perpendicular to the segment at its
midpoint.
Perpendicular lines
Two lines that intersect to form right or 90˚
angles.
Plane
NOT DEFINED, only described:
Extends without ending and has no
thickness and no edges. We usually picture
a plane by drawing a four-sided figure.
NOT DEFINED, only described:
A dot that doesn’t have size, but does have
some size.
Point
Points of
Concurrency
Polygon
Postulate
Pythagorean
Theorem
A closed plane figure formed by three or
more segments such that each segment
interacts exactly two other segments only
at their endpoints and no two segments
with a common endpoint are collinear.
EX. Angle Addition Postulate :
Little Angle + Little Angle = Big Angle
A statement that is accepted without proof.
In a right triangle, the sum of the squares of
the legs is equal to the sum of the square of
the hypotenuse.
Quadrilateral
Ray
Starts at an endpoint and goes in any
direction without ending.
Reflection
A transformation in which a line of
reflection acts like a mirror, reflecting
points to their images.
Remote Interior
Angles
An interior angle of a polygon that is not
adjacent to the exterior angle.
Right angle
An angle with measure of 90°.
Right triangle
A triangle with one right angle.
Rotation
A transformation that turns a figure about a
fixed point a number of degrees.
Same-side interior
angles
Two interior angles on the same side of the
transversal.
*When 2 parallel lines are cut by a
transversal, same side interior angles are
supplementary.
Scalene triangle
A triangle with no congruent sides.
Segment of a line
Two points on the line and all points
between them.
Segment bisector
A line, segment, ray, or plane that
intersects a segment at its midpoint.
Sine
Skew Lines
Lines that are not coplanar and do not
intersect.
Straight angle
An angle measure of 180°.
Supplementary
angles
Two angles whose measures have the sum
of 180°.
Tangent
Theorem
Transformation
EX. Vertical Angle Theorem:
Vertical Angles are congruent.
A statement that has been proven.
A change in position, size, or shape of a
figure.
Translation
A transformation that moves every point in
the figure the same distance in the same
direction.
Transversal
A line that intersects two or more coplanar
lines in different points.
Triangle
A figure formed by three segments joining
three non-collinear points.
Vertex of an angle
The common endpoint in an angle.
Vertex of a triangle
Each of the three points of the triangle.
120
Vertical angles
The nonadjacent angles formed by two
intersecting lines.