MODERN GEOMETRY2.4, 2.5, 3.1

THOMPSON

POLYHEDRA - PRISMS

POLYHEDRA - PYRAMIDS

CYLINDERS, CONES, & SPHERES

THE PLATONIC SOLIDS

EULER’S CHARACTERISTIC

PERIMETER

The perimeter of a polygon of the sum of the lengths of its sides.

PERIMETER –INDUCTIVE REASONING WITH TOOTHPICKS

n equilateral triangles

TRIANGLEALTITUDES

I. The altitude of a triangle is its height.

h

TRIANGLEALTITUDES

I. The altitude of a triangle is its height.

II. It is segment from a vertex, perpendicular to the opposite side.

h

TRIANGLEALTITUDES

I. The altitude of a triangle is its height.

II. It is segment from a vertex, perpendicular to the opposite side.

III. May lie outside of triangle.

h

SIERPINSKI’STRIANGLE

SIERPINSKI’S CARPET

0 1 2 3 4Stage:

243in2

AREA

bhA bhA21

AREA

bhA )( 2121 bbhA

AREA

h

PhA21

h is called

“apothem”

EUCLIDEAN CONSTRUCTIONS

MEASURED CONSTRUCTIONS

CLASSWORK / HOMEWORK

Classwork Constructions

Quiz (Extra Credit) on Thursday