11.3 curves, polygons and symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · a...
TRANSCRIPT
![Page 1: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/1.jpg)
11.3 Curves, Polygons and Symmetry
![Page 2: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/2.jpg)
Polygons
![Page 3: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/3.jpg)
Simple
DefinitionA shape is simple if it doesn’t cross itself, except maybe at theendpoints.
![Page 4: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/4.jpg)
Closed
DefinitionA shape is closed if the endpoints meet.
![Page 5: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/5.jpg)
Polygon
DefinitionA polygon is a simple closed curve where all sides are line segments.There are no arcs allowed.
![Page 6: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/6.jpg)
Concave v. Convex
DefinitionA polygon is convex if any segment connecting any two points in theinterior of the curve lies entirely inside the curve.
DefinitionA polygon is concave if any segment connecting two points of theinterior of a curve passes outside of the curve
![Page 7: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/7.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3
triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 8: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/8.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle
4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 9: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/9.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4
quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 10: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/10.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5
pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 11: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/11.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6
hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 12: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/12.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7
heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 13: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/13.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8
octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 14: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/14.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9
nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 15: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/15.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10
decagon11 hendecagon12 dodecagonn n-gon
![Page 16: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/16.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11
hendecagon12 dodecagonn n-gon
![Page 17: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/17.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12
dodecagonn n-gon
![Page 18: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/18.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn
n-gon
![Page 19: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/19.jpg)
Classification of Polygons by Sides
Number of Sides Polygon Name3 triangle4 quadrilateral5 pentagon6 hexagon7 heptagon8 octagon9 nonagon10 decagon11 hendecagon12 dodecagonn n-gon
![Page 20: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/20.jpg)
Regular Polygons
DefinitionA regular polygon is a polygon where all sides and interior angles arecongruent.
What is the name of a regular triangle?
•
• •What is the name of a regular quadrilateral?
• •
• •
![Page 21: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/21.jpg)
Regular Polygons
DefinitionA regular polygon is a polygon where all sides and interior angles arecongruent.
What is the name of a regular triangle?
•
• •What is the name of a regular quadrilateral?
• •
• •
![Page 22: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/22.jpg)
Regular Polygons
DefinitionA regular polygon is a polygon where all sides and interior angles arecongruent.
What is the name of a regular triangle?
•
• •What is the name of a regular quadrilateral?
• •
• •
![Page 23: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/23.jpg)
Exterior Angle Sum
What is the exterior angle sum for a square?
What is the exterior angle sum for a pentagon?
Conjecture?
Exterior Angle Sum
The exterior angle sum for a convex polygon is 360◦
![Page 24: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/24.jpg)
Exterior Angle Sum
What is the exterior angle sum for a square?
What is the exterior angle sum for a pentagon?
Conjecture?
Exterior Angle Sum
The exterior angle sum for a convex polygon is 360◦
![Page 25: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/25.jpg)
Exterior Angle Sum
What is the exterior angle sum for a square?
What is the exterior angle sum for a pentagon?
Conjecture?
Exterior Angle Sum
The exterior angle sum for a convex polygon is 360◦
![Page 26: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/26.jpg)
Exterior Angle Sum
What is the exterior angle sum for a square?
What is the exterior angle sum for a pentagon?
Conjecture?
Exterior Angle Sum
The exterior angle sum for a convex polygon is 360◦
![Page 27: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/27.jpg)
Triangle Classifications
We can classify triangles in two ways - by the number of congruentsides and by the types of angles. What types of triangles are there?
Types of TrianglesBy Side By Angle
scalene no congruent sides acute all angles acuteisosceles at least two congruent sides right one right angle
equilateral all sides congruent obtuse one obtuse angle
Important to note: your book correctly states that a triangle that isequilateral is also isosceles. Some books incorrectly say that these aredisjoint descriptions.
![Page 28: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/28.jpg)
Triangle Classifications
We can classify triangles in two ways - by the number of congruentsides and by the types of angles. What types of triangles are there?
Types of TrianglesBy Side By Angle
scalene no congruent sides acute all angles acuteisosceles at least two congruent sides right one right angle
equilateral all sides congruent obtuse one obtuse angle
Important to note: your book correctly states that a triangle that isequilateral is also isosceles. Some books incorrectly say that these aredisjoint descriptions.
![Page 29: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/29.jpg)
Triangle Classifications
We can classify triangles in two ways - by the number of congruentsides and by the types of angles. What types of triangles are there?
Types of TrianglesBy Side By Angle
scalene no congruent sides acute all angles acuteisosceles at least two congruent sides right one right angle
equilateral all sides congruent obtuse one obtuse angle
Important to note: your book correctly states that a triangle that isequilateral is also isosceles. Some books incorrectly say that these aredisjoint descriptions.
![Page 30: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/30.jpg)
Quadrilateral Classifications
That we want to do here is list all properties we know about thedifferent quadrilaterals. Included in these properties we want to pointout are:
if opposite sides are parallel
if opposite sides are congruent
if opposite angles are congruent
if adjacent angles are congruent
if adjacent sides are perpendicular
if diagonals bisect each other
if diagonals are perpendicular
if diagonals are congruent
if there is at least one pair of parallel sides
if there is at least one pair of congruent sides
![Page 31: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/31.jpg)
Parallelogram
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
![Page 32: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/32.jpg)
Parallelogram
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
![Page 33: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/33.jpg)
Rectangle
opposite sides congruentopposite angles are congruentdiagonals bisect each otheropposite sides are paralleldiagonals are congruentadjacent sides are perpendicular
![Page 34: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/34.jpg)
Rectangle
opposite sides congruentopposite angles are congruentdiagonals bisect each otheropposite sides are parallel
diagonals are congruentadjacent sides are perpendicular
![Page 35: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/35.jpg)
Rectangle
opposite sides congruentopposite angles are congruentdiagonals bisect each otheropposite sides are paralleldiagonals are congruentadjacent sides are perpendicular
![Page 36: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/36.jpg)
Rhombus
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
adjacent sides congruent
![Page 37: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/37.jpg)
Rhombus
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
adjacent sides congruent
![Page 38: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/38.jpg)
Rhombus
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
adjacent sides congruent
![Page 39: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/39.jpg)
Square
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
diagonals are congruent
adjacent sides are perpendicular
adjacent sides congruent
![Page 40: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/40.jpg)
Square
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
diagonals are congruent
adjacent sides are perpendicular
adjacent sides congruent
![Page 41: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/41.jpg)
Square
opposite sides congruent
opposite angles are congruent
diagonals bisect each other
opposite sides are parallel
diagonals are congruent
adjacent sides are perpendicular
adjacent sides congruent
![Page 42: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/42.jpg)
Kite
two pairs of congruent adjacent sides
diagonals are perpendicular
one pair of congruent angles
![Page 43: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/43.jpg)
Kite
two pairs of congruent adjacent sides
diagonals are perpendicular
one pair of congruent angles
![Page 44: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/44.jpg)
Trapezoid
at least one pair of parallel sides
![Page 45: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/45.jpg)
Trapezoid
at least one pair of parallel sides
![Page 46: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/46.jpg)
Isosceles Trapezoid
at least one pair of parallel sides
at least one pair of congruent sidesbase angles congruent
![Page 47: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/47.jpg)
Isosceles Trapezoid
at least one pair of parallel sides
at least one pair of congruent sidesbase angles congruent
![Page 48: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/48.jpg)
Isosceles Trapezoid
at least one pair of parallel sides
at least one pair of congruent sidesbase angles congruent
![Page 49: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/49.jpg)
Hierarchy for Triangles
For triangles, here is the relationship between them based on sides.
Triangle
Scalene Triangle Isosceles Triangle
Equilateral Triangle
![Page 50: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/50.jpg)
Hierarchy for Quadrilaterals
Can you come up with a similar diagram for quadrilaterals?
Quadrilateral
Kite Trapezoid
Parallelogram Isosceles Trapezoid
Rhombus Rectangle
Square
![Page 51: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/51.jpg)
Hierarchy for Quadrilaterals
Can you come up with a similar diagram for quadrilaterals?
Quadrilateral
Kite Trapezoid
Parallelogram Isosceles Trapezoid
Rhombus Rectangle
Square
![Page 52: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/52.jpg)
Symmetries
1 Line symmetry2 Rotational symmetry3 Point symmetry
![Page 53: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/53.jpg)
Line Symmetry
Line SymmetryA figure has line symmetry if we can draw a line that divides thefigure in half. We can think of this as the line over which we can foldthe figure to make it fold onto itself.
![Page 54: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/54.jpg)
How Many Lines of Symmetry?
![Page 55: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/55.jpg)
How Many Lines of Symmetry?
![Page 56: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/56.jpg)
Rotational Symmetry
Rotational (Turn) SymmetryA figure has rotational symmetry if we can rotate the figure somenumber of degrees less than 360◦ and get the same exact polygonback in the same orientation.
We describe the property as α degrees of turn symmetry.
![Page 57: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/57.jpg)
Rotational Symmetry?
![Page 58: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/58.jpg)
Rotational Symmetry?
![Page 59: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/59.jpg)
Point Symmetry
Point Symmetry
Point symmetry is the term that we use when a figure has 180◦ turnsymmetry.
Which of our figures have point symmetry?
![Page 60: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/60.jpg)
Diagonals
DiagonalA diagonal is a line segment that joins to nonadjacenet vertices.
The question is, how many diagonals does a convex polygon have?
Number of Diagonals
A convex polygon with n sides we have n(n−3)2 diagonals.
![Page 61: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/61.jpg)
Diagonals
DiagonalA diagonal is a line segment that joins to nonadjacenet vertices.
The question is, how many diagonals does a convex polygon have?
Number of Diagonals
A convex polygon with n sides we have n(n−3)2 diagonals.
![Page 62: 11.3 Curves, Polygons and Symmetrybtravers.weebly.com/.../6729909/curves_polygons_and... · A polygon is concave if any segment connecting two points of the interior of a curve passes](https://reader036.vdocuments.mx/reader036/viewer/2022071218/605205fd9d90056613218f90/html5/thumbnails/62.jpg)
Diagonals
DiagonalA diagonal is a line segment that joins to nonadjacenet vertices.
The question is, how many diagonals does a convex polygon have?
Number of Diagonals
A convex polygon with n sides we have n(n−3)2 diagonals.