1. Geometry Objectives 6 – 8 Part 1
TAKS Tutorial
Geometry Objectives 6 – 8
Part 1

2. Welcome to part 1 of the Geometry Objectives tutorial.
Today, we will cover the topics:
Using Algebra to solve problems involving basic geometric definitions
Pythagorean Theorem
Patterns
Transformations
Coordinate Geometry

3. Part 2 of the tutorial over these objectives will be on Tues, April 15 for 10th grade and Wed, April 16 for Exit Level
Remember, “8th grade” geometry is covered on the 10th grade TAKS and High School Geometry is covered on the Exit Level.

4. Topics covered next time for the Exit Level will be:
Special Right Triangles
Segment-Angle Relationships
Circle segments & Arclength
Parallel & Perpendicular Lines
Dimensional Changes
2D & 3D Figures & Relationships
Please be sure to attend this very important session on April 16!

5. The topic of Measurement has already been covered.
You may find the power point lessons and their corresponding worksheets on Mrs. Nelson’s website.

6. This problem was on the 2006 test.
With this figure they provide a table of values.
This problem is so much easier if you look in the table for patterns!

7. Let’s study the table.
The value of x, water depth, increases by 1 each time.
The surface of the water is the circle at the top of the cone
It’s difficult to see the pattern to the y-values, Area of water surface
Let’s get some common denominators—easier to see patterns!

8. Let’s study the table.
Now that all of the denominators are the same, look at the numerators.
They each have ∏.
And the x-value squared gives the coefficient of ∏.
The pattern seems to be that Area is

9. Now, let’s check out the answer choices.
Which choice shows x2 multiplied to pi over 16?

10. This problem was on the 2003 test.
Notice, this time you didn’t get a table of values---so make one of your own!

11. What is the independent variable?
What is the dependent variable?
Stage #
# Circles
Stage # 1 1 2 3
# of circles 3 7
Now, look for that pattern. Or better yet, look at the options! n ?

12. Use your calculator and the options until you find a match for this graph.
Enter each option into y= on the calculator, go to the table, and find the match.
Stage #
# Circles 1 7 3 2 ? n
FYI: 2n is entered as 2^x

13. This problem was also on the 2003 test
This problem was also on the 2003 test. It covers a basic Geometry definition with an Algebra twist.
Complementary angles are 2 angles whose measures add up to be 90o.
Now, eliminate the two options that do not use 90o.
So, you have to ask yourself, what do I know about complementary angles?

14. mA + mB = 90
Replacing mA with x, I get
x + mB = 90
Subtracting x from both sides of the equation, I get
mB = 90 – x
Since complementary angles add up to be 90o, I can write…

15. April 2006
What do you notice about the relationship of the hose to the side of the garden?
The hose is perpendicular to one side, forming 2 congruent right triangles.

16. As soon as you recognize that you have a right triangle, you should be thinking of how you can apply the Pythagorean Theorem.
Check the formula chart. The Pythagorean Theorem formula is there. b a
a2 + b2 = c2 c

17. We were told that each side of the equilateral triangle is 11 ft.
That means that
c = 11 ft and
a = ½ of 11 = 5.5 ft
a2 + b2 = c2
(5.5)2 + b2 = (11)2
b2 = (11)2 – (5.5)2
b2 = 121 – 30.25
b2 = 90.75 b a
5.5 c 11
Find the square root of 90.75!

18. Here are the answer choices:

19. Transformations are always tested.
You could be asked about:
Translations
Reflection
Rotation
Dilation
So, you have to be prepared for any one of them. Remember, dilations can also include any kind of similar polygon problem or one that talks about scale factor.

20. This one was on the 2006 test.
Note: The 10th grade TAKS usually only have one kind of transformation per problem and reflects over the x-axis or the y-axis.

21. Use your calculator and graph y = -x so you know what it looks like
Use your calculator and graph y = -x so you know what it looks like. Find some points from the table and draw the line on your paper.
Note: You are only looking for the image of point M, so use that point only. You do not need to use the entire parallelogram.

22. You need to move from M perpendicular to the line
You need to move from M perpendicular to the line. The line has slope -1, so you move with slope 1.
From (6, 3), you need to translate (slide) down 4 units.
From M to the line was 4.5 diagonals. Now, move 4.5 diagonals past the line.
You now are at the point
(6, -1)
That will now bring you to (6, 3). Note that answer is there just in case you stop too soon. You are not finished with the problem yet!

23. Look for the point (6, -1) in the answer choices
Look for the point (6, -1) in the answer choices. These are the coordinates of M’

24. This problem was on the 2003 test
This problem was on the 2003 test. See how they have you work several problems all in one? Aren’t they sneaky?

25. Let’s check out the first option: Rotate the figure 90o around M.
Here is the visual. The rectangle is filled in.
Next, it is rotated 90o around M.
No vertex is at the origin (0, 0) so eliminate choice A.

26. Let’s check out the second answer choice: Reflect the figure across the line x = 1.
Here is the visual. The rectangle is filled in and the line x = 1 is marked.
Next, the figure is reflected across x = 1.
No vertex is at the origin (0, 0) so eliminate choice B.

27. Let’s check out answer choice C: Reflect the figure across the line y = 2.5.
Here is the visual. The rectangle is filled in and the line y = 2.5 is marked.
Next, the figure is reflected across y = 2.5.
No vertex is at the origin (0, 0) so eliminate choice C.

28. That leaves answer choice D: Don’t assume
That leaves answer choice D: Don’t assume! Translate the figure left 6 and then down 5.
Here is the visual. The rectangle is filled in.
Next, the figure is translated left 6.
Then, it is translated down 5.
Point N is now at the origin (0, 0) so choice D is the answer.

29. This problem was on the 2006 test.

30. Down 3 and right 2 a second time
Study the graph.
Find the point (0, 0).
Look for point S.
Draw a ray from (0, 0) through S.
The point you are looking for MUST be on this ray
This point MUST, since the scale factor is 2, move the distance between the origin and S past S.
Down 3 and right 2
Down 3 and right 2 a second time
That brings us to (4, -6)

31. And the answer is…

32. There are a few problems on you paper for you to practice what we learned today.