Unit 7- Symmetry
This unit is about line and rotation symmetry, similarity of polygons, enlargements and reductions and scale factor.
Enlargements, Reductions and Scale Diagrams
Definitions
- ENLARGEMENTS- An increase in the dimensions of an object by a constant factor. The shape can be 2D or 3D.
- SCALE FACTOR- The constant factor by which all dimensions of an object are enlarged or reduced in a scale drawing.
- REDUCTIONS- A decease in the dimensions in an object by a constant factor. The shape can be 2D or 3D.
- SCALE- A comparison between the actual size of an object and the size of it's diagram. It can be expressed as a fraction, ratio or percent, or in words or a diagram. The scale 1:32 means that one centimeter on the diagram represents thirty two centimeters on the real object.
- SCALE DIAGRAM- A drawing that is similar to the actual figure or object. It may be smaller or larger than the actual object, but it must be the same proportions.
- PROPORTION- A relationship that shows two ratios are are equal. It can be written as a fraction or ratio. The ratio 1 girl to 4 students is the same as 5 girls to 20 students. 1/4 = 5/20 or 1:4 = 5:20.
Scale Diagram of a Scroll
The scale is 1:3. One centimeter on the diagram is three centimeters on the real object.
The scale is three. To get the real object, you would have to multiply the dimensions of the diagram by three.
The diagram is to scale. 2:4.5 is the same as 6:13.5. It is proportional.
The scale is three. To get the real object, you would have to multiply the dimensions of the diagram by three.
The diagram is to scale. 2:4.5 is the same as 6:13.5. It is proportional.
Similar Polygons
-Polygons are similar if the interior angles are the same and the sides are proportional.
Similar Polygons
http://www.mathopenref.com/similarpolygons.html
-When two triangles are similar, the interior angles must be the same or the sides must be proportional.
Line Symmetry
-Line Symmetry is when identical halves can be reflected in a vertical, horizontal or oblique (Slanted) line of symmetry.
A line of symmetry is also known as a line of reflection.
-A translation is a slide along a straight line. It can be expressed as words, (Two units down, two units to the left), as abbreviations, (R3, D2), or as symbols with arrows.
-A rotation is when a shape rotates around a point.
-A shape has rotational symmetry when an object can fit into itself more than once in a complete turn.
-Order of rotation is the number of times a shape can fit into itself in one complete turn.
-Angle of rotation is the minimum measure of an angle needed to turn a shape into itself. It may be measured in degrees or fractions of a turn. It is equal to 360 / the order of rotation.
-A rotation is when a shape rotates around a point.
-A shape has rotational symmetry when an object can fit into itself more than once in a complete turn.
-Order of rotation is the number of times a shape can fit into itself in one complete turn.
-Angle of rotation is the minimum measure of an angle needed to turn a shape into itself. It may be measured in degrees or fractions of a turn. It is equal to 360 / the order of rotation.