Geometry Chapter 20

Geometry is the study of shapes Geometry is a way of thinking about and seeing the world. Geometry is evident in nature, art and culture. What geometric objects do you see in this picture?

Geometric Vocabulary Point – An exact location in space Line – An endless collection of points along a straight path Line segment – Part of a line that begins at one point and ends at another. The points are called the endpoints of the segment..

Geometric Vocabulary Ray – Part of a line that has one endpoint and extends endlessly in the other direction Plane – An endless, flat surface that is named by any three points not on the same line. ( length and width, no thickness).A.B.C

Geometric Vocabulary Parallel Lines – Lines do not intersect but are in the same plane Intersecting Lines – Lines meet at one point Perpendicular Lines – Lines form a right angle

Angles An angle is formed when two rays have the same endpoint. This endpoint is called the vertex. The two rays that form the angle are called sides.

There are four types of angles – Right angle Forms a square corner Forms a 90 degree angle. – Straight angle Forms a straight line Angle is 180 degrees – Acute angle Forms an angle that is less than a right angle Angle is less than 90 degrees – Obtuse angle Form an angle that is more than a right angle Angle is more than 90 degrees 90° 180 °

OPEN & CLOSED FIGURES A CLOSED FIGURE/SHAPE starts and ends at the same point. An OPEN FIGURE/SHAPE does NOT start and end at the same point. CLOSEDOPEN ● ● ● Start End Start End

POLYGON POLYGONS are 2-dimensional shapes. A POLYGON is a “closed” shape (all the lines connect). A POLYGON is made up of line segments that do not cross. The number of sides gives a POLYGON its name. POLYGONS NOT POLYGONS

Plain Geometry A triangle is bounded by three straight lines, a quadrilateral by four, and a pentagon by five straight lines. A quadrilateral is a polygon. In fact it is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on. A square is a quadrilateral in which all the sides are equal, and all the angles are right angles. A parallelogram is a quadrilateral whose opposite sides are parallel. A regular polygon has equal sides and equal angles.

Triangles Equilateral, Isosceles and Scalene There are three special names given to triangles That tell how many sides (or angles) are equal. There can be 3, 2, or no equal sides/angles: What type of Angle? Triangles can also have names that Tell you what type of angle is inside: Combining the Names Sometimes a triangle will have two names, for example:

Quadrilaterals Quadrilateral just means "four sides" (quad means four, lateral means side). Any four-sided shape is a Quadrilateral. But the sides have to be straight, and it has to be 2-dimensional. Special types of quadrilaterals:

Shape Properties Properties of Quadrilaterals

Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in... It is called three-dimensional, or 3D because there are three dimensions: width, depth and height. There are two main types of solids, "Polyhedra", and "Non-Polyhedra"

Polyhedra A polyhedron is a solid made of flat surfaces. Each surface is a polygon.polyhedron Platonic Solids Prisms Pyramids

Definitions Face - Any of the individual surfaces (flat sides )of a solid object. Base - The lowest part. A special face. The surface that a solid object stands on, or the bottom line of a shape such as a triangle or rectangle. Edge – the line segment where two faces meet. Vertex - A point where two or more straight lines meet. Corner. face

Platonic Solids There are five platonic solids Tetrahedron 4 Faces 4 Vertices 6 Edges Cube 6 Faces 8 Vertices 12 Edges Octahedron 8 Faces 6 Vertices 12 Edges Dodecahedron 12 Faces 20 Vertices 30 Edges Icosahedron 20 Faces 12 Vertices 30 Edges Images courtesy of Wikipedia

Prism

Prism Examples

Pyramids Parts of a pyramid There are many types of pyramids, and they are named after the shape of their base. and so on….

Non-Polyhedra Sphere Facts: It is perfectly symmetrical. It has no edges or vertices. It is not a polyhedron. All points on the surface are the same distance from the center. Torus Facts: It can be made by revolving a small circle along a line made by another circle. It has no edges or vertices. It is not a polyhedron. Cylinder Facts: It has a flat base and a flat top. The base is the same as the top, and also in-between. It has one curved side. Because it has a curved surface it is not a polyhedron. Cone Facts: It has a flat base. It has one curved side. Because it has a curved surface it is not a polyhedron.

Marshmallow Shapes In your classroom, you can build geometric shapes using marshmallows and toothpicks. What do the marshmallows represent? The toothpicks? basic shapes cube square pyramid

References geometry.html geometry.html mothering.com/marshmallow-buildings.html