unit 1 Day 7:

Day 7:similar triangles
Explanation:http://www.youtube.com/watch?v=ffHKcLu5Zac
Two triangles are similar if the only difference is size.

These triangles are all similar:

 

Quiz:
1)
Find whether the triangles shown are similar.

2)
Find if the pair of triangles shown is similar.

3)
ΔUVW and ΔXYZ are similar. If w = 10, z = 5, x = 4, and y = 3, find the remaining side lengths.

 key:
1)

The angles whose measure is given are not equal.
Hence, we have to compute the measures of the other angles.

In the first triangle, taking x as the measure of unknown angle, the sum of the measures of the three angles of the triangle is:


Subtracting 96 from both sides of the equation.

Similarly for the other triangle
Let the measure of two unknown angles, which are given to be equal, be y each.


Subtracting 82 from both sides of the equation


Dividing both sides of the equation by 2, we get:

As corresponding angles are not equal, the two triangles are not similar.

2) The measure of one angle is equal to 50 degrees in both triangles.

The other marked angles are not equal.
We have to compute the measure of the third angle to check if they have the same measure.

In the first triangle taking x as the measure of unknown angle the sum of three angles of the triangle is


Subtracting 120 degrees from both sides of the equation:

Similarly for the other triangle, let the measure of unknown angle be y.
The sum of the measures of the three angles is:


Subtracting 100 degrees from both sides of the equation.


Hence, the other two corresponding angles do not have the same measure.

As corresponding angles are not equal, the two triangles are not similar.

3) Writing a proportion for the lengths of corresponding sides, we get:

Using cross products, we get:


Dividing both sides by 5, we get:

Writing a proportion for the lengths of corresponding sides, we get:


Using cross products, we get:


Dividing both sides by 5, we get:

Unit 1 day 6:

Day 6: Angles in similar triangles.
Explanation:http://www.youtube.com/watch?v=s4fr9vC9C5Q&feature=player_embedded#!
Examples:Triangles are similar if they have the same shape, but not necessarily the same size. You can think of it as "zooming in" or out making the triangle bigger or smaller, but keeping its basic shape. In the figure above, as you drag any vertex on triangle PQR, the other triangle changes to be the same shape, but half the size. In formal notation we can write

which is read as "Triangle PQR is similar to triangle P'Q'R' ".

Quiz:

Key:

1)D

2)D

3)B

1

Marks: --/1

Determine which of the following triangles are similar.

Choose one answer.

	a.
	b.
	c.
	d.

Question2

Marks: --/1

The minimum condition for the similarity of two triangle is that

Choose one answer.

	a. any one angle must be equal and two corresponding sides must be in the same proportion.
	b. at least two corresponding sides must be in the same proportion.
	c. all three corresponding angles must be equal.
	d. at least two corresponding angles must be equal.

Question3

Marks: --/1

Similar triangles always have

Choose one answer.

	a. the same perimeter.
	b. the same shape.
	c. the same area.
	d. all of these.

unit 1 Day 5:

Day 5: similar figures ,what are they and finding missing lengths.
Similar figures-Two geometrical objects are called similar if they both have the same shape. More precisely, one is congruent to the result of a uniform.
Explanation-http://youtu.be/rsK6pbqU6uo
Examples-

Finding the missing lengths-http://youtu.be/1UuiF3mskQA
Examples:

Quiz :
1)Old Faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height of a nearby tree that casts a shadow 63 feet long? Assume the triangles are similar.

2)Rob enlarged a 4 in. wide by 7 in. tall picture into a banner. If the banner is 3.5 ft wide, how tall is it?

A. 6.05 ft

B.6.125

C. 7 ft        

D. 7.125 ft

3)A painting 40 in. long and 56 in. wide is to be scaled to 10 in. long to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar?

Key:
1)Tree Old Faithful

_x =_60 height 63 42 shadow
42x = 60(63) Find the cross products. 42x = 3,780 Simplify.
x = 90 Divide each side by 42. The tree is 90 feet tall.
 2)B

3)The painting displayed on the poster should be 14 in. long.

unit 1 Day 4:

Day 4: students will b able to identify surface area in real life.
Explanation:There are many real-life problems that involve finding areas, buying carpet, laying a hard-wood floor, painting or wallpapering a room, to name a few.
Examples:
1)pouring liquids into a container.

                                                                                                   2)If you want to paint a house, you need to know the surface area to determine how much paint to buy.

3)If you want to plant grass on a dirt lot, you need to know the surface area to determine how much grass seat to use.

4)If you want to sew a dress, you need to know the surface area of the dress (dress size) to know how much material you need.

5)If you want to make money mowing lawns, you need to know the surface area of the lawn to know how much to charge for the work.

.

6)If you want to put carpet in a living room, you need to know the surface area of the room to know how much carpet you will need.

Quiz:

1)Give 2 more examples of real life surface area.

Unit 1:Day 3

Day 3:Surface area
Explanation:http://www.youtube.com/watch?v=0A0qhoh-aYc
formulas for surface area:

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

 (h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r ²) + (2 pi r)* h

Surface Area of a Sphere = 4 pi r 2

 (r is radius of circle)

Surface Area of Any Prism

  (b is the shape of the ends)
Surface Area = Lateral area + Area of two ends
(Lateral area) = (perimeter of shape b) * L
Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

Examples:

Quiz:

1)
Find the surface area of a cone with a radius of 3 and a slope of 2.

2)find the surface area of a cylinder with a radius of 15 and a slope of 22.

3)find the surface area of a sphere with the radius of 77.

key:

 1)118.849557522123895 square units

2)23487.1681415929206 square units

3)4506.01769911505square units