The Ithaca High School Geometry Blog

Here are answers to the practice exam I gave you on the last day of class.  Let me know if you think I made a mistake–I’m human, after all!

1. 3       2. 2       3. 2       4. 1       5. 2       6. 2       7. 4

8. 4       9. 1     10. 3     11. 3     12. 1     13. 4     14. 3

15. 3     16. 2     17. 4     18. 2     19. 2     20. 1     21. 2

22. 2     23. 4     24. 3     25. 2     26. 3     27. 4     28. 3

Now for the free-response questions:

29.  (x + 2)↑2 + (y – 4)↑2 = 2.25
30.  perimeter = 100
31.  perimeter = 30
32.  3 √2
33.  12
34.  (1, 0)
35.  y = -x + 1
36.  36
37.  27 π
38.  For this proof, show that triangles PAL and REG are similar (they are congruent, actually), then state that corresponding sides of similar triangles are proportional, then cross-multiply to convert the proportion into the given multiplication.

You probably noticed that I had to fudge a couple of the mathematical figures, due to the limitations of this weblog (and my limitations in figuring out how to overcome them!)

Other notes and comments:

• The proof that you will have to do for your exam is, I think, easier than the one shown here.
• This practice test did not include andy coordinate geometry proofs, which you need to be able to do.
• You also need to know how to find the area of a regular polygon.
• You must be able to do constructions using compass and straightedge.  Refer to the packet I gave you in class last week.
• If I remember correctly, much of the class struggled with the angles in circles.  Might I politely suggest that would be a topic worth reviewing?

As demonstrated in this practice exam, knowledge of 30-60-90 triangles and 45-45-90 triangles and the ratio of their sides is beneficial, as is the Pythagorean Theorem. This practice exam did not test any trig.  We probably will.

Review Session:  Monday a.m. from 9 until about 11:30.  You do not have to be there the entire time, but you will need a pass to get in.

Exam:  Monday afternoon at 12:45 in the gym.  Be there or be a quadrilateral that is both a rhombus and a rectangle!

For Thursday’s test, you will wish you knew…

How to measure to the nearest millimeter

How to find the area of a regular polygon

How to find the area of a parallelogram

How to find the area of a trapezoid

How to find the area of a sector

How to find missing dimensions of a figure given the area

How to find the area of a right triangle given one leg and the hypotenuse

How to find the radius and/or the apothem of a regular polygon using trig

How to find the length of an arc

How to find the area of a figure if you know the area of a similar figure and the ratio of their sides

How to find the area of a triangle in the coordinate plane

How to find the shaded area between two geometric figures, say for example a square and a circle which are internally tangent to each other

Here is a summary of most of the ideas that will be tested on Wednesday.

Definitions–like the quiz, you will be able to use a clearly labeled picture in lieu of a written definition.

Find measures of angles, including for cyclic (inscribed) quadrilaterals

Find measures of arcs

Find measures (lengths) of segments

Prove triangles are similar and that their sides are proportional

Write the equation of a circle and graph a circle given an equation

Show that a line is/is not a secant or a tangent to a circle

Here are the answers to the quiz:

1. By the converse of the Pythagorean Theorem, 10²  + 24² = 26² , so AB is perpendicular to CB, so YES, AB is tangent to circle C.

2. NO. Don’t trust the diagram! The segment BC looks like the hypotenuse of right triangle, but the hypotenuse of this triangle is the supposed tangent segment. Since 5²  + 13²  is not equal to 12² , angle CAB is not a right angle.

3. 100°

4. 80°

5. 260°

6. 180°

7. 3

8. 7

Great job on the Regents’ Math A Exam!

The class average was 82.3, the median score was 83.  This is the scaled score, not a straight average, of course.  Twenty of you students earned scores of 85 or better, which is the Regents’ standard for ‘Honors’.  This is twice as many as I had in my three sections of Geometry last year.

I was really pleased how hard you worked all the way to the end of the review sessions.  Your dedication to hard work and success is what makes teaching you such a pleasure!

I’m really looking forward to our second semester together.

–Mr. J

There will be a review session for the Regents’ Math A Exam on Thursday morning beginning at about 8 a.m. in room H214.  Come in with all your questions and concerns.

I will also be at school and generally available all day Tuesday and Wednesday morning for extra help or to take a test that you are missing.

You should be at the school Thursday between 12:30 and 12:45 to take your exam.  Remember that my classes, because we are special, get to take the exam in York lecture hall instead of the cafeteria.  Please don’t be late–don’t make me call your Mom!

Thursday’s test will include some transformational questions; some on coordinate geometry from the past two weeks like slope, distance and midpoint, point-slope form of the equation, parallel/perpendicular lines, etc; a bit on parabolas; and also soving systems of equations.  There will be a page or two on the test devoted to each separate topic, but I may just mix them up to mix you up.

Don’t forget, there will be fudge(s) [What is the plural of 'fudge'?  Whatever it is, there will be several kinds] on Thursday, so don’t be tempted to start your vacation until you have taken  a piece or two plus your test!

And it’s not too late to request your favorite fudge flavor!

Here is URL for the textbook’s website:

www.classzone.com/cz/books/geometry_2007_na/book_home.htm?state=NY

Just copy and paste the address into your browser.

When you get to the website, check out the vocabulary flipcards in the games and activities sections, and also the  Animations.  The flipcards are a great way to learn and/or review the vocabulary without having to make your own set of cards.  In the Animation section, there is an animation for lesson 4.8 that is a great way to learn and review the various transformations.  There are also some decent animations for chapter 9 as well, although some go into more detail than we will in our brief overview of this topic.

As with most websites, these features work best if you have something faster than a dial-up connection (like I do at home).

Hi everybody who is bored enough at home today to check my edublog!

I know you are all as disappointed as I am that we didn’t have school today, but we just have to take these things as they come.

I’ve kept busy today grading tests and fun stuff like that. I’m sure you’ve been just as productive as I have.

Okay, truth be told, I took a two-and-a-half hour nap this afternoon, and man, did it feel great! Slept right through both geometry classes!

Below is part of what I was going to assign for homework today, if I hadn’t slept through class. It is vocabulary, and I’m not planning on checking or collecting it. Honestly. However, it is in your best interests to know these words, and one of the best ways to learn vocabulary is to write out the words and what they mean. More than just reading the definition, the process of manually writing out the meanings forces your brain to process the ideas one or two steps further than if you just look at ink on a page. And then you remember them better.

Hope this help keep you from being so bummed about missing geometry class today.

Chapter 9—Properties of Transformations
Vocabulary Assignment #1

Some of the vocabulary comes from Lesson 4.8 starting on page 272 and from Lesson 6.7 starting on page 409.

Define or make a sketch of the following terms:

Transformation
Coordinate notation for a translation
Image
Translation
Reflection
Rotation
Congruence transformation
Dilation
Reduction
Enlargement

Our next chapter will be Chapter 9:  Properties of Transformations, but we are only going to hit the highlights.  We will explore basic definitions of translations, reflections, rotations, dilations, and symmetry, which will involve some coordinate graphing.  Speaking of graphing, we will also be starting our preparation for the Regents’ Math A Exam by reviewing coordinate geometry including graphing lines, distances, slopes, midpoints, and parallels and perpendiculars.  Then we will look at graphs of parabolas and circles.  It may seem, some days, that what we cover has nothing to do with what we went over yesterday, but in the end it will all come together.  We will be taking a test on the last day before the holiday break , but I will make fudge (chocolate, peanut butter, what do you want?–leave a comment) for you for that day to help ease your pain.