Point
a location in space that has no size or shape
How do you name a point?
with one uppercase letter and a dot
Line
a set of points that go forever in 2 directions that has to be perfectly straight (no curves) or a never-ending straight path
How do you name a line?
using 2 points with the line symbol above them or with a cursive lower case letter beside the line
Line Segment
a part or a piece of a line that has a beginning and an end (with no arrows on the ends)
Endpoints
the beginning and the end
How do you name a segment?
using the two endpoints and the segment symbol
Ray
a part or piece of a line that has only one endpoint and goes forever in one direction (one point on one end and an arrow on the other)
How do you name a ray?
using the endpoint and one other point on the ray with the ray symbol
symbol for a ray
a straight line with one arrow on only one end
symbol for a segment
what is generally termed as a straight line above the letters; the endpoint MUST be the first letter
symbol for a line
a line with arrows on both ends
Plane
a flat surface that goes forever in all directions
name a plane
you need three letters, but the three letters must make a triangle shape or with a cursive uppercase letter
you can see the plane goes on forever by
naming a plane with three letters in a TRIANGLE
symbol for plane
there is no symbol. you must write out the full word
only term without a specific symbol
a plane. you must write out the full word
What does a cursive lowercase letter and what does a cursive capital letter stand for?
a cursive lower case letter stands for a line and a cursive capital letter stands for a plane
Angle
a figure formed when two rays have a common endpoint (∠ is the sign)
Vertex
the common endpoint of the rays that form an angle
How are angles named?
using three letters (but the middle letter HAS to ALWAYS be the vertex) and the angle symbol (∠), if there is only one angle name it using only the vertex, or with a number (ex: ∠ 3)
angle symbol
∠
When naming an angle, where is the vertex?
it must be the middle letter or it could stand alone
Degree
unit of measure (°)
degrees are in a full circle and the sum of the exterior angles of all polygons
360 °
angles and circles
measured with degrees
Protractor
a tool used to measure angles in degrees
Acute Angle
an angle that is more than 0° and less than 90°
Right Angle
an angle that is exactly 90°
Obtuse Angle
an angle that is more than 90° and less than 180°
Straight Angle
an angle that measures exactly 190° (it is straight) (m ∠ 2 is "the measure of the angle")
Parallel
lines on the same plane that never intersect
is parallel to" symbol
I I
Perpendicular
lines (or segments or rays) intersect to form right angles
sign for perpendicular
⊥
Skew
lines that are not in the same plane, not intersecting, not parallel, and not perpendicular
skew lines always found
on something 3D
Complementary Angles
angles whose measures add up to 90°
Adjacent Angles
two angles that share a common ray and are "right next to each other
Supplementary Angles
angles whose measure add up to 180°
Congruent
same size and shape
symbol for "is congruent to
≅
Vertical Angles
form when two lines intersect; are "opposite" each other; are congruent
classify a triangle
by their sides and by their angles
triangle
formed by the three line segments that intersect only at their endpoints
right triangle
a triangle with ONLY ONE right angle (other two are acute)
diagonal
a line segment that connects two nonconsecutive (not adjacent) vertices of a polygon
acute triangle
a triangle with 3 acute angles
vertices
plural of vertex
polygon
a closed plane figure made of line segments that meet at their endpoints to form vertices and are not curved
obtuse triangle
a triangle with one obtuse angle (other two are acute)
alternate interior angles
between the parallel lines (interior) and on opposite sides of the transversal, and not adjacent (alternate). ARE CONGRUENT
alternate exterior angles
outside the parallel lines, on opposite sides of the transversal. NOT ADJACENT, ARE CONGRUENT
corresponding angles
located in the same position on each of the parallel lines
isosceles
a triangle with at least two congruent sides
scalene
a triangle with NO congruent sides (all sides a different length)
equilateral
a triangle with THREE congruent sides and they are also equiangular (all sides the same length) can ONLY be ACUTE (ARE ALSO ISOSCELES)
equiangular
all angles congruent
isosceles triangle symbol
Δ
sum of a triangle's interior angles
180°
quadrilateral
a four-sided polygon
trapezoid
a quadrilateral with exactly one pair of parallel sides
parallelogram
a quadrilateral with exactly two pairs of parallel sides and congruent OPPOSITE sides
regular polygon
any polygon with all sides congruent (equilateral) and all angles congruent (equiangular)
translation
a transformation that moves a figure horizontally, vertically, or diagonally. also called a "slide
slide
another name for translation
reflection
a transformation that "flips" a figure across a line (a mirror image)
rotation
a transformation that turns a figure around a point. the point of rotation can be on the figure, outside the figure, or inside the figure
line of symmetry
a line drawn through a figure that creates two halves that are mirror images of each other (that are congruent to each other)
similar figures
two figures that are the same shape, have congruent corresponding angles, but are different sizes
is similar to" sign
∼