Tips from the Pros

Tips From the Pros: Ladder Safety

The link will take you to the video!!!

http://www.youtube.com/watch?v=lQ_ufvdb1MU 

Unit 1: Day 8

Day 8: Scale factor of sides and Scale factor of area

This lesson reflects what was taught about similar triangles, but can be applied to all shapes. 

Let's start with a simple example. To find out the scale factor from the smaller rectangle to the larger rectangle, you take 2 corresponding sides and put them in a ratio. For this the 2 ratios would be 20:24 and 10:12. Simplify both ratios and you get 5:6, and 5:6. This means that they are similar and he scale factor is 5/6. So, if all you had was the large rectangle, you could multiply is by 5/6 and get the small rectangle. 

Another example: 

The maker of the this picture took the ratios of 6:9 and 8:12. The resulting ratio is 2:3. they got 2/3 because a ratio is the same as a fraction, and 1.5 because that's 9 divided by 6.

 

Scale factor of area is a bit more complicated. Lets take this as an example:

The area of the rectangle now is 10 cm². If we take a scale factor of 2, the dimensions become 10cm by 4cm, or 40 cm². Even though each side was multiplied by 2, the area was increased 4 times. With a factor of 3, it would be 15 cm by 6cm, but the area would be 90 cm². Overall, whatever the scale factor is, square it. Volume is the same, but cube the dimension instead.

 

 

Just another example of how scale factor works!

Quiz Time!

1. If I increase this by a scale factor of 2, what is the area?

2. What is the simplified side ratio of the heights of the horses?

3. What is the length of  both the unknown lenths given the shapes are similar?

Just another example of how the scale factor works with

 

 

Key:

 

 

1. The original area is 36 cm², so using the scale factor of area, we double the dimensions. That would be 18 cm and 8 cm. This is 144 cm², or 4 times the area of the original shape.

 

 

2. First you have to convert the heights to the same unit. I did 5 x 12 so that the bigger horse would be in inches. The fraction is 5/60. Simplified, this is 1/12.

 

 

3. The missing length EF is 6.5 cm, and the missing length AB is 5 cm. I found that because our 6:12 ratio, the only one we're given, tells us that the smaller one is half the size of the larger. one. 

 

Unit 1:Day 6

Day 6: Similar Triangles

Similar triangles work the same way as any other shape, but you can also use angles with triangles. 

 

 

If the angles are the same, the triangles are similar.

Matching amounts of arcs mean that they are the same angle. All of the above are similar.

Even though the shapes aren't the same size and may be rotated, the shapes, like the ones above, will most likely be similar.

 

 

Quiz Time!

 

1. Are the triangles similar?

2. What is the measure of the missing angles?

 

3. Are the triangles similar?

 

Key:

 

1. The triangles are similar because they share the same angles

 

 

2. The missing angles are 70 and 80

 

 

3. The triangles are similar because the two edges are parallel. 

 

 

 

Unit 1: Day 7

Day 7: Similar Triangles

This lesson will focus on the 3 methods of determining if triangles are similar:

SSS
SAS
AAA

SSS: SSS means Side Side Side. If all of the sides are congruent, the triangle is similar

SAS: SAS means Side Angle Side. If you have 2 congruent sides and one common angle, you can be sure the triangles are similar. 

AAA: AAA means Angle Angle Angle. If the triangles have the same 3 angles, you know they're similar. If the problem only provides 2 angles, you still know all the angles are the same because they add up to 180. 

Just some extra info

And to see the video we made, click on the link!!!

http://www.youtube.com/watch?v=JSLWonT8re4

Quiz Time!

1. Are these triangles similar?

2.Are these triangles  similar?

3. Are these triangles similar?

Key:

1.  Yes, because the angle measurements add up to 180 degrees. 

2. Yes. When I used the cross multiplication method, I substituted one of the variables for X,  to see if it would come up with the equal and congruent length, which it did. 

3. Yes,  because the angle measurements are the same, and the two side lengths are similar. 

Unit 1:Day 6

Day 6: Similar Triangles: Angle to Angle

 

 

This method of determining if shapes are equal is specific to triangles. It's a lot simpler than other shapes; you don't have to make a fraction and cross- multiply. It's simply this: If the triangles' angles are the same, they are similar.

 

In these triangles, even though one is rotated, we know they are similar because they share 2 angles.

This one is more complex because you only have one angle provided. However, it is still easily solvable. Take the 2 side length from each triangle and put them both in a ratio. 21:14 and 15:10 both simplify to the ratio of 3:2, and that along with the shared angle tells us that they're similar.

Just another example.

Quiz Time!

 

1. Are these triangles similar?

 





 

2. What is the angle of C?

 

 

3. What is the length of x? Are the triangles similar?

 

 

 

 

 

 

Key:

 

1. The triangles are similar because the angles all correspond.

 

 

2. Angle C is 70 degrees.

 

 

3. Side x is 24 meters long. We got that because the side 4 was multiplied by 4 to get 16, so the 6 must also be multiplied by 4. The triangles are similar. 

 

Unit 1: Day 5

Day 5: What are Similar Figures and finding different lengths

A lot of today will mimic the lesson from day 2 with dilations and similar figures

Similar figures help us find the size of a bigger or smaller shape if we have at least 2 dimensions. 

The dimensions you use to prove the figures are similar can be any of the following 

• 2 side lengths
• Area and a side length
• 2 angles (in polygons besides squares/ rectangles)
• An angle and the area
• Any other 2 measurments

From there you set up a fraction: x = x

                                                 y    y

and cross- multiply to find the unknown variable or find if 2 shapes are the same. 

Once you find this, you can use the math to find other unprovided measurments.

For example, if the half- circles are similar, you could then use that information to find the area and perimeter of the triangle.

Quiz Time!

 1. Find the height of the tree.

2.Are these triangles similar?

3. What is the length of x?

Key:

1. 15 ft tall ( put the two fractions equal to each other and solve by cross multiplication) 

2. Yes, the ratio is 1:2 

3. 12 cm (use the cross multiplication method)

Unit 1: Day 4

Day 4: Using the equations from Day 3

 Prism: To find the SA of a prism, combine the area of the 2 bases and the area of the sides. 

Pyramid:To find the SA of a pyramid, take the base area, and add 1/2 x base perimeter x slant height.

Cylinder: To find the SA of a cylinder, take the area of the bases and add 2πrh (radius and height).

Cone: To find the SA of a cone, take the area of the base and add πrL (radius and slant height).

Sphere: To find the SA of a sphere, use the equation 4πr².

Youtube Video!

Quiz Time!

1. What is the SA of this cone given

s=16

h=9

r=4

2. Find the SA of the basic prism

3. Find the SA of the sphere given the radius is 13.

ANSWERS TO THE QUIZ: 

1. The surface area of the cone is 251. 2 units squared (Area of base + 3.14 R S) 

2. The surface area of the rectangular prism is 72 feet squared ( area of all sides) 

3. The surface area of the sphere is 2122.64 units squared. (4* 3.14* R squared)