Download Math 9 Study Guide Unit 7 Unit 7 - Similarity and Transformations

Math 9
Study Guide
Unit 7
Unit 7 - Similarity and Transformations
Review about triangles and angles:
1. 3 angles add up to 1800
2. Equilateral triangle – all angles equal, all sides equal
3. Isosceles triangle – 2 angles equal, 2 sides equal
Enlargement makes something larger (scale factor larger than one)
Reduction makes something smaller (scale factor less than one)
Scale Diagram: enlargement or reduction of an original diagram and has matching
or corresponding lengths
Scale Factor: how much bigger or smaller a diagram is compared to the original
Scale factor can be given as a decimal or a fraction.
If you are given a diagram with dimensions and the scale factor and asked to
draw the scale diagram multiply each dimension by the scale factor to find out the
dimensions of the scale (new) diagram.
Scale factor can also be expressed as a ratio (ex. 1:150)
Similar Polygons
Polygons: have many sides
Similar polygons: have same shape but not necessarily the same size (can be an
enlargement or reduction)
When angles match they are called corresponding angles.
When sides match they are called corresponding sides.
When the SF (scale factor) is the same for all sides and the angles are equal we
say the diagrams are similar.
Math 9
Study Guide
Unit 7
Properties of Similar Polygons
When polygons are similar:
1. The corresponding angles are equal.
AND
2. The corresponding sides are proportional (scale factors are equal)
Therefore, if two polygons have corresponding angles that are equal and
corresponding sides that are proportional they are similar
Remember: When finding the scale factor (SF), be sure to compare the
corresponding sides.
Math 9
Study Guide
Unit 7
Similar Triangles
To determine if triangles are similar, we only need to look whether:
1. The corresponding angles are equal.
OR
2. The scale factors are the same.
Transformations
Line of Symmetry/Line of Reflection: divides a shape into 2 or more congruent
parts (same shape and size). There is no line of symmetry if a line will not make 2
equal parts.
Equidistant : equal distance from line of symmetry
Tessellation: repeats same shape over and over (no overlap of shapes)
To make a reflection on a line of symmetry the reflection (new diagram) must be
the same distance from the line of symmetry and must be the same shape as the
original shape.
Each point on one side of the line of symmetry must have a corresponding point
on he other side of the line.
Math 9
Study Guide
Unit 7
Rotations and Rotational Symmetry
Rotational Symmetry (RS): property of a shape that coincides (matches) with
itself after a rotation of less than 3600 about its center.
No shape has a RS of 1 because every shape coincides with itself after 3600 . RS
must be 2 or more.
Order of Rotation: the number of times a shape coincides with itself during a
rotation of 3600 .
Angle of Rotation Symmetry: least amount required for a shape to rotate and
coincide with itself.
Center of Rotation: point on shape where rotation happens when finding out if the
shape has rotation symmetry. Can be in the center or on a vertex (corner).
Identifying Types of Symmetry on the Cartesian Plane
Translation (slide): a transformation that moves an entire shape or point to a new
location on the same flat plane
When a shape and its transformation image are drawn the resulting diagram may
show:
• no symmetry
• line of symmetry
• rotational symmetry
• both line and rotational symmetry