Name: _____________________________Date: _____________________________

CHAPTER 7 NOTES – Similarity and Transformations

Date: 7.1 – Scale Diagrams and Enlargements ________________7.2 – Scale Diagrams and Reductions ________________7.3 – Similar Polygons ________________7.4 – Similar Triangles ________________7.5 – Reflections and Line Symmetry ________________7.6 – Rotations and Rotational Symmetry ________________7.7 – Identifying Types of Symmetry on the Cartesian Plane ________________

Review: ________________ Test: ________________

What You’ll Learn

7.1/7.2 – Draw and interpret scale diagrams7.3/7.4 – Apply properties of similar polygons7.5/7.6/7.7 – Identify and describe line symmetry and rotational symmetry

What are some careers that require either the construction or analysis of scale diagrams?

Read over the ‘What Should I Recall’ section on pgs. 316 & 317 of the text and note anything important below.

_______________7.1 – Scale Diagrams and Enlargements__________________________Focus: Draw and interpret scale diagrams that represent enlargements.Main Ideas:

Warmup: Look at the digital camera drawings on the bottom of p. 318.a) How are the twodrawings alike?b) How are they different?c) Using the grid, counteach side length and foreach set of sides, write the fraction:

d) Write each fractionas a decimal. What doyou notice about thesenumbers?

What is a scale diagram?

What are correspondinglengths?

What is scale factor?

What is proportion?

What is an enlargement?

What is a reduction?

Ex1Use a ruler to determine the scale factor of the diagram.

*To calculate scalefactor, the units youmeasure each diagram Original diagramwith must be the same. Scale diagram

Ex2A scale factor for an

enlargement is .

If the scale diagramhas a length that is 60cm, what is the actual length of the original?

Ex3Draw a scale diagramof the drawing. Usea scale factor of 1.5

Reflection: When you are given a scale factor, how do you know if it is an enlargement or a reduction. Use a couple examples to help explain.

_______________7.2 – Scale Diagrams and Reductions____________________________________Focus: Draw and interpret scale diagrams that represent reductions.Main Ideas:

Warmup: What is a scale diagramreduction? Use the terms ‘original diagram’and ‘scale diagram’ inyour definition.

When are scale diagramreductions used insociety?

How can you tell bythe scale factor thatyour scale diagram isa reduction?

What’s another way towrite a scale factor?

Ex1Use a ruler to find thescale factor.

scale diagram

original diagram

Ex2A scale factor for a reduction of a chair

is 1 : 8 (same as ).

If the height of the chairis 75cm, what is theheight on the scaledrawing?

Ex3Draw a scale diagramof the drawing.Use a scale factor of 0.6.

Reflection: What are two ways to write a scale factor? Explain using examples.

______________________7.3 – Similar Polygons__________________________________________Focus: Recognize and draw similar polygons, then use their properties to solve problems.Main Ideas:

Warmup: Look at the right sideof p.347. What is alike about the twotriangles, and what isdifferent? You should use the word ‘angles’and the word ‘sides’ atsome point during your answers.

What is a polygon?

What does similar mean?

What is a similar Polygon?

Ex1Look at the similarpolygons on the bottomof p.335. Read the 3 lines at the bottom ofthe page.a) What do you noticeabout correspondingangles?b) Can you find a common theme for the

corresponding sides?

What is another namefor the common ratio produced by the corresponding sides? What do all similarpolygons have in common?

Ex1 BFind the missing sides 130 40cm C B’and angles A 90 110 20cm C’

30cmKeep the scale factor A’as a fraction and use 50cm 125 Dcross-multiply. 85

E 80cm D’

45cm

E’

Ex2Do Example 3 on p.339of the text. Don’t lookat the solution untilcompleted.

Ex3Are the polygonssimilar?Use your ruler to checkso that you can be certain.

Reflection: How do you know when two polygons are similar. Use proper vocabulary in your explanation.

_______________________7.4 – Similar Triangles__________________________________________Focus: Use the properties of similar triangles to solve problems.Main Ideas:

Warmup: What are the The measure of the corresponding angles ___________________________.characteristics of ANDsimilar polygons from Corresponding sides:yesterday?

Both of the above two conditions must be true before we can call two polygons similar.

How is it different for Triangles are polygons, but they are a special type of polygon. If yousimilar triangles? know that one of the two conditions is true for two triangles, you

can say that the triangles are similar:

OR

Read ‘Connect’ on p.344 of the text and note anything you feelis important.

Ex1The triangles are similar. Write math statements forcorresponding angles,corresponding sides, and that the trianglesare similar.

Ex2Find the missing sides.

Ex3The two triangles are similar. Find the height of the tree.

Ex3The two triangles aresimilar. Find the Amissing lengths.

11.4m 6.2m

C B D

9.6m 4m

E

Reflection: How do you go about matching up the corresponding sides for similar triangles?

____________________7.5 – Reflections and Line Symmetry__________________________________Focus: Draw and classify shapes with line symmetryMain Ideas:

Warmup: Draw any lines of symmetry for the following shapes.How many does eachhave?

S What is another namefor a line of symmetry?

Ex1Go to p.355 in the textand see if you cananswer example 2without looking atthe solution.

Ex2 Draw the reflectionimage of ΔABC Athrough the followingreflection lines:i) vertical line through 2 on the x-axisii) horizontal line B Cthrough 2 on the y-axisiii) oblique line AC

Fill out the tables below.

i) ii)

iii)

Point ImageA A’B B’C C’

Point ImageA A’B B’C C’

Point ImageA A’B B’C C’

Reflection: How do you identify whether a shape has a line of symmetry?

___________________7.6 – Rotations and Rotational Symmetry______________________________Focus: Draw and classify shapes with rotational symmetry.Main Ideas:

Warmup: Put your pencil in the Centre of the shape.Rotate the tracing onecomplete turn aboutyour pencil, countingthe number of times the rotation coincideswith the original shape,and write this numberdown.

What is rotationalsymmetry?

What is ‘order ofrotation’?

What is the ‘angle ofrotation symmetry’?

What shapes do nothave rotational symmetry?Give an example.

What is a transformation?

Ex1 a) b) Determine if the shapehas rotational symmetry, and if it does, state the orderof rotation and theangle of rotationsymmetry.

c)

Sometimes, the pointof rotation is not themiddle of the shape.

Ex2 a) Rotate the triangle270 clockwiseabout the point (2, 1) b) Rotate the triangle180 clockwise aboutthe point (5, 1)c) 180 counter clockwise about the origin

Reflection: When you are being asked to rotate an image, what specifics must you first know?

__________7.7 – Identifying Types of Symmetry on the Cartesian Plane________________________Focus: Identify and classify line and rotational symmetry.Main Ideas:

Warmup: Look at Example 1 onp.369 (don’t look at solutions).For each of a, b, and c,determine whether theyare related by linesymmetry, rotationalsymmetry, or both.Then give specifics about their symmetry.

Ex1Cover p.371, and do a)example 2 on p.370 byfirst copying the imageonto the grid.

b)

Point ImageA(-1,1) A’B(3,1) B’C(3,0) C’D(-1,0) D’

Point ImageA(-1,1) A’B(3,1) B’C(3,0) C’D(-1,0) D’

For part c, a translationmeans to move each c)corner of the shape by what is indicated.

For part c in the lastexample, what is another way to writethe translation 4 unitsright and 1 unit down.What’s another wayto write 3 units left and5 units up?

Ex3a) Draw the following shape on the grid:A(1, 4), B(3, 6), C(3, 2),D(6, 3)b) Translate the shape by L8, D7 and redrawand complete the tablec) Is there any line orrotational symmetryin the completeddiagram?

Point ImageA(-1,1) A’B(3,1) B’C(3,0) C’D(-1,0) D’

Point ImageA(1,4) A’B(3,6) B’C(3,2) C’D(6,3) D’

Reflection: What do you have to practice most about transformations (translations, reflections, and rotations)? Explain.