Week 8 Flashcards
Polygon
Closed planar (2D) figure made up of line segments joined end to end, with no crossings or reuse of endpoints
Bounded by 3 or more edges
Line segment
Piece of a straight line between two endpoints
Polygonal region
Face of a polygon, often just called by the polygon that bounds it, ie. face of a cube called square instead of square region
Diagonal of a polygon
Line segment joining two vertices of the polygon that are not joined by a side (non-adjacent vertices)
Equiangular polygon
Polygon whose angles all have the same size
Equilateral polygon
Polygon whose sides all have the same length
Regular polygons and example
Polygons which are both equiangular and equilateral ie. square is a regular quadrilateral
What does a quadrilateral have?
4 angles, 4 sides, 4 vertices
What does a pentagon have?
5 angles, 5 sides, 5 vertices
What does a hexagon have?
6 angles, 6 sides, 6 vertices
What does a heptagon have?
7 angles, 7 sides, 7 vertices
What does an octagon have?
8 angles, 8 sides, 8 vertices
What does a nonagon have?
9
What does a decagon have?
10
Acute triangle
Largest angle measures less than 90 degrees
Right triangle
One angle measures 90 degrees
Obtuse triangle
One angle measures more than 90 degrees
Scalene triangle
Sides all have different lengths
Isosceles triangle
At least two sides have the same length
Equilateral triangle
All three sides have the same length
Square
A rectangle that is also a rhombus (two consecutive sides of equal length and other two sides also of equal lengths AND both pairs of opposite sides parallel)
Rhombus
A kite (quadrilateral with two consecutive sides of equal lengths and the other two sides also of equal lengths) that is also a parallelogram (both pairs of opposite sides parallel) A SYMMETRICAL KITE
Rectangle
A parallelogram (both pairs of opposite sides parallel) with a right angle
Parallelogram
A type of trapezoid with both pairs of opposite sides parallel
Kites
A quadrilateral with two consecutive sides of equal lengths and the other two sides also of equal lengths
Trapezoid
A quadrilateral with only one pair of opposite sides parallel
Isosceles trapezoid
Trapezoid with both the angles next to one of the parallel sides the same size
Perpendicular
Lines that form right angles at their point of intersection
Acute angle
Angle whose measure is between 0 and 90 degrees
Obtuse angle
Angle whose measure is greater than 90 but less than 180 degrees
Straight angle
Measures 180 degrees
Adjacent angles
Angles with the same vertex and a common side between them
Supplementary angles
Two angles whose sides add up to 180 degrees - can be adjacent too
Complementary angles
Two angles whose sizes add up to 90 degrees
Exterior angle of a polygon
Formed by the extension of one side of the polygon through a vertex of the polygon and the other side of the polygon through that vertex
Interior angle or angle of the polygon
Angle inside a polygon
Bisector of an angle
A ray that cuts a given angle into two equal angles
Perpendicular bisector
A line that intersects a line segment at its midpoint, forming a 90 degree angle
Convex polygon
All diagonals are contained in the polygonal region (looks like each angle goes outward)
Concave polygon
A polygon with an interior reflex angle (angle collapses in)
A square is always a rectangle T/F
True
A rectangle is always a square T/F
F
A rhombus is a trapezoid T/F
False
A rhombus is a parallelogram T/F
True
Adjacent edges meet at a
Vertex
Edges are
Straight line segments
A circle is a polygon T/F
False
Perigon angle
360 degrees or full rotation
Reflex angle
An angle that measures between 180 and 360 degrees
Sum of interior angles of any n-gon is
(n-2) * 180
Triangles interior angles sum to
180 degrees
Quadrilaterals interior angles sum to
360 degrees
Interior angles of a regular n-gon measure
(n-2) * 180
__________
n
Congruent
Two polygons are congruent if one can be rotated, translated, or reflected so that the polygons’ edges and vertices all line up (size must be the same)
Congruent polygons can be different sizes T/F
False
Conjecture (or hypothesis)
A general conclusion about some quality of an object that is drawn from a number of individual facts about this quality. A conjecture still needs to be proven, i.e. shown to be true or false. In mathematics we are interested in making a conjecture that tells us more about an object or relationships with other objects.
Definition
The least number of properties of something that must be given to identify that something.
Theorem (or rule)
A conjecture that has been proven true. Often the proof of a theorem involves using definition(s).
Axioms
Self-evident truth statements
Counter-example
Disproves a conjecture
