Geometry

Geometry

 (At the bottom of the page are printable Geometry help notes.)

In our Geometry unit we will be learning about 2-dimensional and 3- dimensional shapes, lines, angles, transformations, coordinates, congruent or similar shapes, perimeter, and area.

 A polygon is a closed figure made of three or more straight line segments.  A regular polygon is a polygon whose sides and angles are equal.

 Below are examples that are not polygons:

  2-dimensional and 3-dimensional shapes can be identified by their properties.  Click on the links below to see the properties of these shapes.

     To learn about the properties of 2-dimensional shapes.

     To learn about the properties of 3-dimensional shapes.

  Below are the types of geometric lines:

      Line –  a line is a series of points that make a straight path on and on in either direction. 

      Ray -   a ray is a straight line that begins at a point and goes on and on in one direction.

      Line Segment -  is the part of a line between two points.

       Horizontal Line -  is a line that runs left to right, like the horizon.

       Vertical Line - is a line that runs up and down, like a telephone pole.

      Parallel Lines - are lines that never intersect and are always the same distance from each other at every point on the lines. 

      Intersecting Lines - are two lines that cross at only one point.

      Perpendicular Lines - are two lines that intersect or meet and make four square or right angles.

 An angle is formed when two rays or line segments meet at a point called a vertex.

 Any angle is a portion of a circle.

 The three angles we will be learning about are right angles which are always 90 degrees, acute angles which are less than 90 degrees, and obtuse angles which are more than 90 degrees.

 A protractor is a tool for measuring the number of degrees in an angle.

  To measure an angle with a protractor follow these steps:

1. Make the lines of the angle longer if necessary.
2. Line up the arrow or hole in the bottom of the protractor with the vertex of the angle.  Remember the vertex is the point where the two lines of the angle meet.
3. Line up the line at the bottom of the protractor with one side of the angle.
4. Decide whether the angle is acute or obtuse to determine which number scale on the protractor to use.
5. Find the number of degrees by finding where the side of the angle goes through a number on the protractor.

 Congruent shapes are the same size and shape.

 Similar shapes are the same shape, but might not be the same size.

  There are 3 basic transformations: slides (translations), turns (rotations), and flips (reflections).

 Remember that when we change the position of a shape it does not create a different shape.  The shape is just in a different position.

 Coordinates are a pair of numbers that locate a point.  Coordinates are always written in the same order, so we call them ordered pairs.  The first coordinate tells the sideways location and the second coordinate tells the up and down location.  Remember go over then up.  In the example below the coordinates are (7,4).

 The distance around a shape is the perimeter.  The length of the perimeter of any polygon is the sum of the lengths of all the sides.

   2 + 2 + 1 + 1 + 1 + 1 = 8

 Area is the amount of space inside a flat (2-dimensional) shape.  Area has two dimensions: length and width.  We measure area in square units.  Area = length x width.

 5 x 5 = 25

  3-dimensional shapes have faces (sides), edges (lines where the sides join together), and vertices (corners).  For example:  the cube below has 6 faces, 12 edges, and 8 corners.

 3-dimensional shapes have three dimensions: length, width, and height. 

 To practice 2-dimensional shapes. 

 To practice 3-dimensional shapes.

 To practice area.   

 To practice comparing area & perimeter.

 To complete an area & perimeter tutorial.  

 To practice using a geoboard.

 To practice transformations. 

 To complete a tutorial on shapes.

 To complete another shape tutorial.  

 To practice using a protractor.

 To practice angles.

Geometric Lines Notes (doc file)

Geometric Lines Presentation (pptx file)

Angle Notes (pdf file)

What's Your Angle? Presentation (ppt file)

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