week 11/18 - 22/2013 geometry 1 pre-ap geometry 1 similarity unit

Week 11/18 - 22/2013

Geometry 1Pre-AP Geometry 1

Similarity Unit

Start of Class….Have your scale drawing on your desk.Get the paper(s) from the front cart.Get 6 pieces of spaghetti and a ruler.

1.Using 3 pieces of spaghetti, create a scalene triangle. 2.Break off another spaghetti noodle to be of equal length to one of the triangle’s sides.3.Break the piece from #2 in half.4.Slide the half from #3 up the triangle, parallel to the side that you measured in #2.

5.When the ends of the spaghetti are tangent to the other two sides while being parallel to the measured side, measure the distances from the point where the spaghetti hits on each side to the vertices. What do you notice about the location of the points of tangency?

6.Complete Steps 2 – 5 using the other two sides. Does your conclusion for #5 hold true for these?

Periods 1 - 6

Tuesday

Hand in worksheet.Can you calculate the value of h in this picture?

h

5.5

Tuesday

Hand in worksheet.Can you find h in this picture?

h

5.5’

Also to be completed…Periods 2, 4, and 6

What if he/she isn’t the midsegment?

h

5’

35’10’h

6’

50’15’

How do you find where the shared angle lies?

h

4’30’

5.5’

h

6’

40’8’

ASSIGNMENT: Shadow Math

For each person in your group:Sketch the similar triangles formed.

Label all vertical and horizontal distances on the triangles.Calculate the height of the school in feet.

Good Day

• Periods 1,3,5: Have your worksheet on your desk.• Periods 2,4,6: Hand in shadow assignment.• Write the answers to these problems on it.1. What is an:

a) orthocenter b) incenter c) circumcenter d) centroid Identify the similarity theorem that will prove the two triangles similar.

2. 3. 4. 5.

18. – 19. Purple or Pink

12

x

Sit with the group you worked with yesterday. On your paper from Tuesday with the group’s building height estimate, complete the following problem.

Jeannie is practicing on the basketball goal outside her house. She thinks that the goal seems lower than the 10 ft. goal she plays on in the gym. She wonders how far the goal is from the ground. She remembers using similar triangles in math so grabs a yardstick and places it so it casts a shadow.

Here are Jeannie’s measurements: Length of shadow cast by goal post and backboard: 5 ft. 9 in. Length of yardstick’s shadow: 1 ft. 6 in.

1.Draw and label a picture to illustrate Jeannie’s experiment.

2.Using her measurements, determine the height from the bottom of the goal post to the top of the backboard.

3.If the goal is approximately 24 inches from the top of the backboard, how does the height of the basketball goal outside Jeannie’s house compare to the one in the gym? Justify your answer.

Turn in your paper to the “In Basket.”

Return to your regularly assigned seats.

Periods 1, 3, and 5

Periods 2, 4, and 6

Happy Thursday!

• Take 10 Fruit Loops and wait patiently for class to begin.• Periods 1,3,5: Have 5 homework problems on desk.

Using the Pythagorean Theorem

Using the Pythagorean Theorem• If h represents the height of the plaza, 1,023 feet, then the hypotenuse of

the triangle is _______ feet.

• Setting up the Pythagorean Theorem would be:

• Converting the answer (in feet) to miles would be approximately _____ miles.

Your assignment is to find the distance to the horizon if you are standing on top of the following. Provide the name of the building and its height (in feet). Show the Pythagorean Theorem formula used to determine the distance and convert it to miles.

• the school• Tallest building in Arizona• the tallest building in the U.S.A.• the tallest building in China• the tallest building in the world

Let’s Make a Foldable Notes

Tangent Ratio

Tangent Ratio (continued)

Sine and Cosine

Remembering What’s What

Discovering Trig Function Relationships

Legend of the Trig Functions

Inverse Trig Functions

The Other Three Trig Functions

Assignment

Look around you in your room, your school, your neighborhood, or your city. Can you find right triangles in everyday objects? List at least ten righ triangles that you find and their location. Draw pictures of at least 3 of them, labeling the right angle that makes the triangle a right triangle. On these 3, measure each of the sides.