5.4 Four-Sided Polygons - Office of Instructionalblogs.fcps.net/.../2016/12/Adv.-Geo-5.4-Four-Sided-Polygons-ppt.pdf · all polygons you work with ... pairs of opposite sides congruent

Advanced Geometry

* are PLANE figures.

* consist entirely of segments (no curves!).

* consecutive sides intersect only at endpoints

* each vertex belongs to exactly two sides.

* nonconsecutive sides do not intersect

* are closed figures.

NOT a polygon!

* are PLANE figures.

3 – D!

* consist entirely of segments -- no curves!

NOT a polygon!

NOT a polygon!

* are closed figures.

NOT a polygon!

* consecutive sides intersect only at endpoints* nonconsecutive sides do not intersect

X

NOT a polygon!

* each vertex belongs to exactly two sides.

P

2

3

1

Definition: In a convex polygon, each interiorangle has a measure less than 180⁰.

Interior angle greater than 180!

NOT convex!

Concave!

For this class, unless stated otherwise, you should assume that all polygons you work with are convex!

Definition: A diagonal of a polygon is any segment that connects two nonconsecutive (nonadjacent) vertices of the polygon.

Quadrilateral: A four-sided POLYGON

QUADRILATERAL

Parallelogram: A QUADRILATERAL with both pairs of opposite sides congruent and parallel

PARALLELOGRAM

Rectangle: A PARALLELOGRAM in which at least one angle is a right angle

RECTANGLE

Rhombus: A PARALLELOGRAM in which at least two consecutive sides are congruent.

RHOMBUS

Kite: A QUADRILATERAL in which two disjoint pairs of sides are congruent.

KITE

Square: A PARALLELOGRAM that is both arectangle and a rhombus.

SQUARE

rectangle rhombus

Trapezoid: A QUADRILATERAL with exactlyone pair of parallel sides.

TRAPEZOID

one pair of parallel sides.

ISOSCELES Trapezoid: A TRAPEZOID in which the nonparallel sides (called legs) are congruent.

ISOSCELES TRAPEZOID

nonparallel sides are congruent

A B

DC

Upper Base Angles: ∡A and ∡B Lower Base Angles: ∡C and ∡D

LegLeg

The parallel sides are the BASES: AB and CD