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Lesson 6 Diggin’ It Develop Understanding

Ready

Use the given information to find the missing sides and the missing angles.

Triangle is a right triangle. Angle is the right angle. Write the exact values for the sides.

1.

a right isosceles triangle with the base of 5 inches. Points are labeled A, B, and C

2.

a right isosceles triangle with the height of 7 times the square root of 2 centimeters. Points are labeled A, B, and C

3.

a right isosceles triangle with the hypotensue of 13 times the square root of 2 meters. Points are labeled A, B, and C

4.

a right isosceles triangle with the hypotensue of 40 feet. Points are labeled A, B, and C

5.

a right triangle with the hypotenuse of 14 centimeters. Points are labeled A, B, and C. Angle B is 30 degrees and angle C is 90 degrees.

6.

a right triangle with the height of 25 meters. Points are labeled A, B, and C. Angle A is 60 degrees and angle C is 90 degrees.

7.

a right triangle with the base of 9 time the square root of 3 feet. Points are labeled A, B, and C. Angle A is 60 degrees and angle C is 90 degrees.

8.

a right triangle with the height of 12 inches. Points are labeled A, B, and C. Angle B is 30 degrees and angle C is 90 degrees.

9.

Find .

a scalene triangle with the side length of 16 feet. The angles are labeled A, B, and C. A vertical line labeled AD cuts the triangle in half.

10.

Find .

a square with side lengths of 11 meters. The angles are labeled A, B, C, and D. A diagonal line labeled AD cuts the triangle in half.

11.

The altitude of an equilateral triangle is How long is each side of the triangle?

12.

The altitude of an equilateral triangle . How long is each side of the triangle?

13.

The side of a square is . How long is the diagonal of the square?

Set

It is possible to identify the location of a point on the edge of a circle in several different ways. One way is to use rectangular coordinates . In this activity you will use a different method. You will be graphing “words” by using letters to identify points around a circle. The size of the rotation or will be the same while the length of the radius will change.

  1. First select a word. Avoid words containing or multiples of . I am choosing the word MATH.

  2. Assign a number to each letter of your word according to the table below.

  3. The numbers correspond to the concentric circles.

  4. You can begin on any spoke.

  5. Move from one spoke to the next in a positive rotation (counterclockwise).

  6. Make a dot at the intersection of the spoke and the circle corresponding with the number of the letter you are on.

  7. Keep graphing the same word until the last letter of the word lands on the spoke that you started on. You will need to make more than one rotation of the circle in order to close your figure.

Circle numbers and their corresponding letters. The letters for “MATH” are underlined.

Circle 1: , D, K, L, N, V, Z

Circle 2: E, U, G, , Q, X

Circle 3: I, C, F, J, , S, Y

Circle 4: O, B, , R, P, W

The word MATH will use the numbered circles 4 1 3 2 in that order. You can begin on any spoke. I began on the spoke with the numbers. I made a dot on 4, rotated to the next spoke and made a dot on 1. I connected the two dots. Then I moved to circle 3, made a dot, connected the segment, and moved to circle 2. You can see MATH marked on the diagram. After marking H, I started over with M on the next spoke. (See the dotted line.) Continue spelling MATH and rotating around the circle until the figure is closed and the path repeats itself. The figure at the right is the completed graph of the word MATH. I always knew MATH was beautiful!

M A T H: 4 1 3 2

4 circles within each other all sliced into 8 even sections. Lines are drawn within the circles creating shapes that look like stars 1234MATHM

The graph of the word MATH.

4 circles within each other all sliced into 8 even sections. Lines are drawn within the circles with points labeled M, H, T, and A1234

Now it’s your turn. Select a word. Short ones are best. Assign the numbers and begin.

14.

Word:

Graph:

4 circles within each other all sliced into 8 even sections. 1234

15.

Word:

Graph:

4 circles within each other all sliced into 8 even sections. 1234

16.

What is the angle between each spoke in the grid above?

17.

How many degrees did it take to graph MATH once? (From M to H?)

18.

How many degrees did it take to graph MATHM? (From M to the M again)

19.

How many times did I need to spell the word MATH to complete the graph?

20.

a.

How many revolutions did it take?

b.

Can you figure out the answer to this question without counting? Explain.

Go

21.

Divide out the common factors.

Perform the indicated operations. Divide out all common factors in your answers.

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25.