Similarity
What two things have to be true for shapes to be considered similar?
Corresponding side lengths have the same scale factor.
Corresponding angles have the same measurements
What form do coordinate rules take?
(x , y)
How do you find the perimeter and area of a rectangle?
To find the perimeter, add all of the side lengths together.
To find the area, multiply the two dimensions together.
When you use the shadow method, what problems might affect the accuracy of your answer?
Too much time between measuring shadows.
No sun :(
Etc.
What is the definition of a ratio?
The comparison of two quantities (numbers).
Define scale factor.
The number you multiply the values of the corresponding sides by.
Does the rule (3x, 3y) create a similar shape to the original rule (x , y)? Explain
Yes! Multiplying both dimensions by the same number.
The dimensions of one rectangle are 3 by 5. Another rectangle has dimensions of 36 by 60. Are the two rectangles similar? Explain.
Yes. The scale factor between both dimensions is 12 and all rectangles have 90 degree angles by definition.
A 2 ft stick casts a 3 ft shadow at the same time, how long would the shadow of a 6 ft person be?
Write a ratio equivalent to 5:9
Lots!
How do you calculate scale factor?
Divide the values of the corresponding sides.
How do you move a shape around but not change its size?
Either add to the x and y values or subtract from the x and y values.
What information does the scale factor actually give you?
It tells you how much bigger or smaller the similar shapes are from each other.
Describe how to use the shadow method.
Tell me :)
What is the definition of corresponding sides?
Sides in the same relative location in two similar shapes. Ex: short side of a rectangle to short side of a rectangle.
If you know one shape's perimeter, how can you use scale factor to find the perimeter of a shape similar to the original?
Multiplying the perimeter of the first shape by the scale factor will give you the perimeter of the second shape.
Does the rule (x+4, 4y) create a similar shape to the original rule (x , y)?
What is the angle sum of a parallelogram? What do you know about a parallelogram's opposite angles?
The angle sum is 360 degrees. Opposite angles are directly across from each other and have the same measure.
Are the shapes made in the shadow method similar?
Yes!
Does scale factor influence the angle measures between two similar shapes?
No.
If you know one shape's area, how can you use scale factor to find the perimeter of a shape similar to the original?
Multiplying the area of the first shape by the scale factor squared (to the second power) will give you the area of the second shape.
Write a rule that moves the original shape (x , y) three units to the right, down seven and a half units, double the width and make the shape half as tall.
(2x+3, 1/2y - 7.5)
The dimensions of two similar rectangles are 2 by 7 and 6 by 21. What is the ratio of the long side to short side in each rectangle? What do you know about those ratios?
7:2 and 21:6. They are equivalent ratios.
A tree casts a 30 ft shadow. At the same time, a 6 ft stick casts a shadow 40 ft long. How tall is the tree?
Good question :)
2The area of one shape is 5 cm2 and the scale factor to a similar shape is 1.5, what is the area of the similar shape? Explain.
1.52 = 2.25
2.25 x 5 = 11.25
Area = 11.25 cm2