Unit 7 - Similarity and Transformations

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Presentation transcript:

Unit 7 - Similarity and Transformations Sections 7.1 and 7.2 Curriculum Outcome: Draw and interpret scale diagrams of 2-D Shapes

Reductions, Enlargements and the Scale Factor Does a map show the actual size of a country? What does it show? What does the legend show us?

Reductions, Enlargements and the Scale Factor An artist’s drawing of an Oxygen (8) atom shows 8 electrons orbiting a nucleus which contains 8 protons (dark spheres) and 8 neutrons (light spheres). If the drawing were to scale, the nucleus would be a minute dot, ten thousand times smaller than it is currently drawn. Can you actually see atoms? How could we represent the ‘scale’ of this image?

Reductions, Enlargements and the Scale Factor Now if the red square is the original drawing, what is the blue square called? What is the yellow square called? How could we determine how many times bigger the blue square is? How could we determine how many times smaller the yellow square is? What do we call that?

Reductions, Enlargements and the Scale Factor The red square has side lengths of 3. The blue square has side lengths of 6. So the enlargement has a scale factor of: Side length of scale drawing Side length of original drawing which reduces to

Reductions, Enlargements and the Scale Factor The red square has side lengths of 3. The yellow square has side lengths of 1. So the reduction has a scale factor of: Side length of scale drawing Side length of original drawing

Reductions, Enlargements and the Scale Factor So what did you notice about the scale factor for an enlargement? What do you notice about the scale factor for a reduction? How do they relate to 1?

Reductions, Enlargements and the Scale Factor The red square has side lengths of 3. The blue square has side lengths of 4. The yellow square has side lengths of 2. What are the scale factors of each? Which factor will be above and below 1? Side length of scale drawing Side length of original drawing Remember a fraction or decimal is okay

Reductions, Enlargements and the Scale Factor The red square has side lengths of 3. The blue square has side lengths of 4. The red square has side lengths of 3. The yellow square has side lengths of 2. Side length of scale drawing Side length of original drawing Side length of scale drawing Side length of original drawing or or

Reductions, Enlargements and the Scale Factor Triangle ABC needs to be enlarged by a scale factor of 3. What do we need to do first? What do we need to do second? 5 4 B 3 C

Reductions, Enlargements and the Scale Factor What do we need to do first? Identify the sides: AB = 4 BC = 3 AC = 5 Now what? 5 4 B 3 C

Reductions, Enlargements and the Scale Factor What do we need to do second? Multiply the sides by the scale factor: AB = 4 x 3 =12 BC = 3 x 3 = 9 AC = 5 x 3 = 15 Now what? 5 4 B 3 C

What do you notice about the new drawing? What about its ‘name’? 5 4 AB = 4 x 3 =12 BC = 3 x 3 = 9 AC = 5 x 3 = 15 Draw the scale drawing. What do you notice about the new drawing? What about its ‘name’? A 5 4 15 B 3 C 12 C’ 9 B’

What do you notice about the new drawing? What about its ‘name’? The new triangle is called A’B’C’ with side lengths: A’B’ = 12 B’C’ = 9 A’C’ = 15 A 5 4 15 B 3 C 12 C’ 9 B’

Triangle JKL needs to be reduced by a scale factor of 0.5. What are the new side lengths of triangle J’K’L’? 9 4 K 8 L

Reduction: Scale Factor: 0.5 JK = 4 9 KL = 8 JL = 9 4 So… J’K’ = 4 x .5 = 2 K’L’ = 8 x .5 = 4 J’L’ = 9 x .5 = 4.5 9 4 K 8 L

So Triangle J’K’L’ now looks like this: 9 4 J’K’ = 4 x .5 = 2 K’L’ = 8 x .5 = 4 J’L’ = 9 x .5 = 4.5 So Triangle J’K’L’ now looks like this: 9 4 K 8 L J’ 4.5 2 K’ 4 L’

What is the original side length in cm of an actual stop sign? This picture of a stop sign is a reduction of a real stop sign…obviously. It is shown at a scale factor of 1:30. The side lengths of the scale drawing are 25mm. What is the original side length in cm of an actual stop sign? STOP

What is the original side length in cm of an actual stop sign? Multiply the side length by the scale factor. 25mm x 30 = 750mm Now convert 750mm to cm. 750mm= 75cm STOP

Assignment Time Section 7.1 Pg. 323/324 #4,5,10, 11 Section 7.2 #4,5,7,8,9,10,11