Week 11: Congruent Triangles - Part II

Like I said in my last post, there is very much to cover with congruent triangles. Thankfully we were able to finish up the new material in class today, so we will be able to have the test as scheduled! To review the material we covered this week in class, I have prepared an interesting assignment. Given what you ought to know about the definitions of quadrilaterals, with diagonals list all sets of congruent triangles (if you have trouble remembering how to find congruent triangles, then take a look at last week's post to review).

For example:

For each type of quadrilateral, I want to see a diagram, a list of the properties of the quadrilateral (label as "given"), a list of sets of congruent triangles, and the total number of congruent triangles. This assignment will be a very helpful tool in studying for next week's midterm exam. As always, if you have any questions, then I will be happy to answer them at any time!


This week's goal:

• Be able to construct proofs of congruent triangles.
• Review properties of quadrilaterals.

Due dates:

• Five unique types of quadrilaterals with their corresponding lists of congruent triangles will be due next week (day of the midterm).

Week 10: Congruent Triangles - Part I

We started a whole new concept with congruent angles, but that was just the beginning. There are many different properties and forms of congruency when it comes to triangles, as I'm sure you have realized in class this week. Do not worry though, because we will be covering more properties of congruent triangles next week, so you will have time then to ask any questions regarding this topic. In case you are struggling with what we covered in class this week, use this page to review the basics of congruency with triangles and go through the proofs on this website to practice solving congruency problems.

For this week's extra credit, I want you to tell me: how many sets of congruent triangles there are (in the picture below), what those triangles are named (make sure they are appropriately listed when making congruent statements), and why they are congruent.

Keep in mind that I created this image from scratch, so if you have any questions or feeling stuck, then let me know! I guarantee I will be able to help (within reason, so do not expect me to give you the answers).


This week's goal:

• Connect properties of congruent angles to properties of congruent triangles.
• Be able to break down a figure that contains multiple congruent triangles.

Due dates:

• The list of congruent triangles and the proofs associated with each one will be due on the day of the test, which will be in two weeks.

Week 9: Congruent Angles

This week in class marks the beginning of a whole new branch of geometry. Congruency is very helpful in many different situations involving geometric problems, and will be a great asset in future math classes. Here is a helpful review link that should catch you up to today (in case you missed anything while in class). Notice that when the two line segments are parallel, the same side angles add up to 180°. I know the different types of angles are not defined, so here is a diagram showing all the definitions we covered throughout the week:

For this week's assignment, construct a "missing angle puzzle" like the one found in this link. I want to see at least ten variables with between one and four angle measurements given. Once the deadline ends for this assignment I will post the received puzzles to the discussion board. Only the students who submitted a puzzle will be allowed to try and solve someone else's puzzle, and I will hand out a prize to anybody whose puzzle was not able to be solved. Now, I will be fair and make sure the puzzles are solvable before posting them to the discussion board, but once they are posted it is fair game.

This week's goal:

• Creatively explore the properties of congruent angles.

Due dates:

• The test has been decided to be in three weeks. The puzzles will need to be submitted by the Friday before the test, or in other words will be due in two weeks.
• For some extra points, the puzzle I gave as an example can be turned in with all angles found. This will be due on the next test date.

Week 8: Ellipses

Circles was fun and all, but we needed to expand our horizons. Ellipses, and elliptical objects are just non-uniformed circles, and after about five weeks of learning formulas and shapes, talking about ellipses doesn't seem so different. It's true we are just covering different types of shapes, but the good news is that this is our last frontier of new shapes! Speaking of frontiers, since this is our last new shape, I think it is appropriate to explore this topic by venturing into the final frontier.

This week's assignment is to play with this tool and make the best effort to find the least number of days as well as the most number of days it takes for 3 revolutions (the tool automatically stops at 3 revolutions). Also, check out this website for a more detailed description of the connection between what we have been covering with orbits and Kepler's laws. The word problems found in the book can be frustrating, but hopefully you will get a better visualization of ellipses and orbits after going through this blog post.

Visualizations can usually be very helpful, and other times they can just add to the confusion. If you are having any problems with ellipses or figuring out what we went through this week, then talk to me! Chances are you are not the only one with the same question.

This week's goal:

• Grasp a clearer visualization of word problems discussed in homework and class
• Familiarize students with meaning behind ellipses

Due dates:

• The records of the most # of days and least # of days for 3 revolutions (including speed and distance when finished) will be due next test date (which will be discussed next week)

Week 7: Circles and Curved Objects

This was a very exciting week, because we finally got to think outside the box! Now that we covered pretty much every angle of polygons and polyhedra, we were able to dig into circles, spheres, and other curved figures. Use this link for reviewing circle stuff, and check out this link for spheres and other objects.

For this week's assignment, you will have to do a little bit of research. Also, it will be broken into two parts involving Earth. The first part is to find the surface area and volume of the Earth using the distance from the center of the Earth to the equator (and assuming the Earth is a perfect sphere). The second part is to list at least 3 famous cities and find the angle from our city to those cities.

Remember, with a sphere you need to find both the latitude and longitude angles. I'll always be willing to answer any and all questions, so if you feel lost or confused then don't feel alone! I can point you in the right direction.

This week's goal:

• Become familiar with the process of the system of global coordinates
• Practice and recognize formulas for circles and spheres

 Due date:

• Hand in work and the angles to other cities by the next test day (which will be decided on in two weeks)