Hello fellow bloggers and mathematicians! 

I can't believe how fast my freshman year has gone by...this will be my last post for this geometry blog! I am happy to be entering summer, but I have really enjoyed all of my classes, teachers, and friends this year. Hopefully it will stay that way for next year!

As a final post, I am going to give the incoming freshmen ten tips for 'surviving' high school...

1. Be yourself

2. Seize new opportunities 

3. Be open to meeting new people

4. Take the classes you want to, not the ones your friends are in

5. Never eat the cafeteria food

6. Try out new/different sports

7. Get involved with as many clubs as you can

8. Don't procrastinate; prioritize

9. Get to know your teachers; be friends

10. Maintain a positive attitude

Throughout this year, I have tried to stay true to these tips. At times I wished that I hadn't procrastinated quite so much or had participated in a bit more, but overall, I did all of these things and had a great year. I hope these tips are helpful to you, even if you're not a freshmen! 

Have a great week and a fantastic summer! (: 

Hello everyone!

Firstly, I would just like to explain that last week Blogmeister was experiencing some technical difficulties, so I was unable to post at that time. The post from both then and the most recent one should be uploaded now.   

Anyways, this week is the beginning of finals for my school! I am very nervous because I've never taken finals before, and I'm not sure what to expect. Wish me luck!

In order to review once again for geometry, I am posting another review questions below. I chose this particular one because I find this area formula hard to remember sometimes, because it doesn't involve side lengths, rather, diagonal lengths.

For this problem, there was a rhombus shown with diagonals of 21 ft and 18 ft. The instructions were to find the area, and the possible answers were as shown: 

a) 378 sq. ft    

b) 189 sq. ft    

c) 162 sq. ft    

d) 27(square root of)85 sq. ft. 

I knew that the formula for the area of a rhombus is 1/2d1*d2, so I substituted in the diameter lengths:

A = 1/2 * 21 * 18 = 189 

With that equation, I was able to find that the area was 189 sq. ft., or answer b. 

I hope this has been a helpful review question! Have a great week! (: 

sinA  =  sinB

   a          b 

Hello everyone!

No, I didn't fall asleep on my keyboard. SOH CAH TOA is actually a helpful trick to use when remembering functions for trigonometry. Basically, the first letter in each triplet stands for a calculator function. The S stands for the key 'sin,' which stands for the term 'sine.' The C stands for the key 'cos,' which stands for the term 'cosine.' Finally, the T stands for the key 'tan,' which stands for the term 'tangent.' Each can be used to find diffent side lengths of a right triangle. 

If you have a given angle measure, or you need to find the measure of an angle, you can use the side opposite as well as the hypotenuse to find it's value using this equation:

sin(angle measure) = opposite side / hypotenuse (hence: SOH)

You can also use the adjacent side and the hypotenuse to find the angle measure, or vice-versa: 

cos(angle measure) = adjacent / hypotenuse (hence: CAH) 

Finally, you can use the opposite side and the adjacent side to find the angle measure, or vice-versa:

tan(angle measure) = opposite side / adjacent side (hence: TOA) 

This can be a confusing process, but through using visuals and writing out the functions, I believe it becomes easier to understand. 

I hope I have helped you understand a little better with this interesting trick! Have a great week! :) 

Hello everyone! Hope you've had yet another fantastic week! 

Today I counted the days left in my school year. There are 30 days including weekends! I am so excited for summer. As much as I have enjoyed my freshman year, I could use a break. Do you have any exciting summer plans? 

On Thursday we took a test in geometry class on the areas of shapes. Below I have listed the formulas for finding the areas of different shapes:

1. Area of a Parallelogram = base * height

2. Area of a Regular Polygon = 0.5 * apothem * perimeter 

3. Area of a Triangle = 0.5 * base * height

4. Area of a Trapezoid = 0.5 * (base 1 + base 2) * height

5. Area of a Rhombus/Kite = 0.5 * diagonal 1 * diagonal 2 

My favorite area formula is for the area of a parallelogram, because it is so easy to remember. What is your favorite? 

Well, so long for now! Good luck in the week ahead of you!

Hello everyone!

I thought the rhyme was "April showers bring May flowers?" Apparently the weather doesn't agree with me, because we're well into May now, and the rain just keeps pouring down! I could really use a bit of sunshine right about now! 

Anyways, since we're working with triangles in geometry, I've been learning about the Pythagorean Theorem. This theorem works for right triangles only. The theorem is as stated:

In this equation, a and b both stand for the legs of the triangle, and c stands for the hypotenuse. It can be very useful when you only know two of the leg measures and need to find the third. Also, if you know that the right triangle is also isosceles, then you would only need one of the side measures to find the other two. 

I hope that this information will be useful to you and that you have a good week! Hope for sunshine! :)

Hello everyone! Happy May!

I hope you've had a fantastic week. I have been quickly getting back into the school routine after having vacation, and everything is going quite nicely.

This week in geometry, we've started a new chapter on shape areas. To start, we went over some patterns found in right triangles that can help you to find the measurements of the hypotenuse and legs. For instance, in a 45º-45º-90º triangle, the hypotenuse will always be the leg times the square root of 2. Also, in a 30º-60º-90º triangle, the hypotenuse will always be twice the shorter leg, and the longer leg will be the shorter side times the square root of three. These patterns have certainly sped things up! They make finding the area to shapes much easier.

I hope I've provided a few unique tricks to help you on your geometry travels! Have a great week! :) 

Hello everyone!

Hope you had a good week...I sure did! Since it was school vacation week, my family and I went to New York City! It was a blast. My favorite part was going to the Top of the Rock! For anyone who remembers, I did a miniature golf course based off of the Rockefellor Center for a geometry project, so it was really cool to be there in person.

This week in geometry, we're having a quest on transformations. We're also starting to review radicals, which we started to learn about last year in algebra. Basically, radicals have to do with square roots. We started off the lesson by doing a worksheet where we had to put radicals into their simplest forms. I had a bit of trouble at first, but I think once I review my square roots some more I'll be fine. 

Hope you have a great week! :) Summer is on its way! 

Hello everyone! 

I hope you had a fantastic Easter! I had a wonderful time with my family. We made a delicious bunny cake!

This week in geometry we learned about a type of transformation called a reflection. Reflections flip the given shape. The two necessary components of a reflection are an object, or preimage, and a line of reflection.

There are two rules of reflections:

Rule One: If a preimage is on the line of reflection, then it will be itself when you find the image.    

Rule Two: The line of reflection is the perpendicular bisector of the segment whose endpoints are A and A prime. 

We also learned about rotations this week, which rotate/turn an image around a specific point. The three components of a rotation are the point of rotation, the angle of rotation, and the direction (either clockwise or counterclockwise). 

I hope that I have helped to give you a basic idea of these two transformations! Have a great week! :) 

Hello everyone!

Easter is coming right around the corner! I can't believe how fast spring has come up. This whole school year has been speeding by! 

In geometry class, we're starting a new unit on transformations. These include translations, dilations, reflections, and rotations. So far, we've reviewed all of them except rotations. Basically, they can be used to change the position/location of a shape. Translations will slide the shape, rotations will rotate it (imagine that!), dilations will make a shape bigger or smaller, and reflections will flip a shape. 

I have found this unit very interesting so far, and I will keep you updated about our progression through it! I wish you all a happy Easter! :)