Unit 7: Similarity – Grade 9 Name:__________________

Sec 7.1: Scale Diagrams and enlargements

A diagram that is an enlargement or a reduction of another diagram is called a scale diagram.

The scale factor is the relationship between the matching lengths on the two diagrams.

To find the scale factor of a scale diagram, we divide: k=lengt hon scalediagramlengt hof original

k=9cm3cm

=3

Note-the units must be the same on the  original and scale diagram- if not, you must convert one to make  them the same- scale factors do not have units

Example #3

A photo has dimensions 10cm by 15cm.

Two enlargements are to be made with each scale factor below. Find the dimensions of each enlargement.

A) scale factor 4

B) scale factor 134

To complete on loose leaf: p. 323 – 324 #'s 4, 5, 6, 11

Sec 7.2: Scale Diagrams and Reduction

A scale diagram can be smaller than the original diagram. This type of scale diagram is called a reduction. A reduction has a scale factor that is less than 1.

Example # 2A top view of a patio table is 105cm by 165cm. A reduction is to be drawn with scale

factor 15 . Find the dimensions of the reduction.

Proportion

 An equation, such as  34=68 , which states that 2 ratios are equal.

Two diagrams are 'proportional' if all sides are multiplied or divided by the same number.

Example #3Which diagram has sides that are

proportional to the original?

Sec 7.3: Similar Polygons

Use Cross Multiplication to solve for the missing variable:

a) 6b=32 b) 10d =5

4

c) 6a=43 d) 2x=

57

e) x3=215 f) 5

6=7y

g) 7b=105 h) 47=m

2

To complete on loose leaf: p. 329 #'s 4 to 11

A Polygon is a closed shape with straight sides. Exactly 2 sides meet at a vertex.

When one polygon is an enlargement or reduction of another polygon, we say the polygons are similar.

When 2 polygons are similar:

 matching angles are equal AND

 matching sides are proportional

To complete on loose leaf: Page 341 #'s 4, 5, 6, 7, 11

Sec 7.3: Similar Triangles

Two triangles are similar if they have the same shape, but different size.

In similar triangles:

matching angles are equal

matching sides are proportional

When writing proportions for corresponding sides, make sure to keep the same triangle on top in each fraction.

To complete on loose leaf: Pages 349 – 350 # 4, 5, 6

Similar Triangles and Word Problems.

To complete on loose leaf: Practice Pages 350 - 351#'s 7, 9, 11, 12, 13, 14

Sec 7.5: Reflections and Lines of Symmetry

line symmetry

 a figure is divided into 2 congruent parts using a line of symmetry (mirror image)

 one half of the figure is reflected exactly onto the other half

 a figure may have more than one line of symmetry

The line of symmetry (also called line of reflection) can be:

horizontal

vertical

oblique

The number of lines of symmetry that can be drawn in a regular polygon is equal to the number of vertices.

Reflecting in the Cartesian Plane:

To complete on loose leaf: Practice Pages 357-359#'s 3, 6, 10

Sec 7.6: Rotational Symmetry Symmetry

Rotational Symmetry

 A figure has rotational symmetry if it can be turned around its center to match itself in less than a 360o turn.

The number of times in one complete turn that a figure matches itself is referred to as:

the order of rotational symmetry

 (triangle has an order of 3)

OR

the degree of rotational symmetry

 (triangle has a degree of 3)

In regular polygons the number of sides is the same as the order of rotational symmetry.

Angle of Rotation Symmetry

 the minimum angle required for a shape to rotate and coincide with itself:

360 °Order of Rotation

What if you know the angle of rotation symmetry and you are asked to find the order of rotational symmetry ?

Examples:

What is the order of rotational symmetry for each angle of rotation symmetry?

A)  90o

B)  120o

To complete on loose leaf: Practice Pages 365-366 #4 to 8

7.7 Transformations in the Cartesian Plane

1. For each pair of shapes, determine whether they are related by line symmetry, by rotational symmetry, by both line and rotational symmetry, or by neither. Describe the symmetry, if any.a) b)

c) d)

2. Which of the rectangles A, B, C, D is related to rectangle X:a) by rotational symmetry about the origin?b) by rotational symmetry about one of the vertices of rectangle X?c) by line symmetry?

3. Identify and describe the types of symmetry in the petal shapes.a) b) c) d) e)

4. Describe the translation below:

To complete on loose leaf: Practice Pages 373-374 #6, 7