This was one of the rare weeks that I’m actually happy with the effort and the progress I made on KA. 😌 I achieved my goal of getting through two unit tests and two exercises, not to mention that for some reason the exercises from the previous unit in Geometry, Transformation Properties and Proofs, went from 100% M.P. down to 80%, so I had to redo that unit test, as well. I’m fairly sure that I studied for more than 5 hours this week, which is probably the first time in a while that that’s happened. The questions I worked through this week were once again all terminology-based, so that was fun… The way a lot of the questions were phrased seemed unnecessarily convoluted and hard to decipher. I got better at interpreting what was really being asked and started to memorize some of the key terms and that made the questions easier to understand. I’m happy to be done with these two units and am hoping that the upcoming units will seem more like math and less like english. 

The first thing I worked on this week was Unit 3’s unit test which was ten questions long. On Tuesday, I made it halfway through the test but then got a question wrong and called it quits for the day. I passed the test on my second attempt on Wednesday getting all ten questions correct in a row relatively easily. Here are five questions from the test:

Unit 3 – Congruence – Unit Test

Question 1

This was the second question I did on Tuesday. As you can see, it was super easy. I was thinking to myself that I wished all the questions were this obvious. Unfortunately, these types of questions were outliers. 👎🏼

Question 2

I would have gotten this question wrong if I hadn’t read the seventh step of the proof before answering. You can see that it essentially gives away the answer by saying, “subtract ∠x from both sides of the question (6).” I was going to choose another answer for the fill in the blank above, but it didn’t make sense with what the seventh step said, so I switched my answer and got it correct. 🙃

Question 3

This was one the of types of questions where I didn’t really know what was going on, so I just went with my gut on what the solution was since I didn’t completely understand. I wrote in my notes that I was about 75% sure of my answer before submitting it, but really, it was just a guess.

Question 4

This was the question I got wrong on Tuesday that made me need to restart the test. 🤬 It seemed to me that the logic applied for this proof could be applied to every triangle (which I still think is true), but I guess the reason why that answer wasn’t correct was because the question gave specific angle measurements and the proof was specifically for this triangle with those given measurements. I think if the question had used variables instead then I would have been correct in saying that the proof could be applied to all triangles. 

Question 5

This question took me about ten minutes to think through. It took me a while, but I realized that lines AD and AC were both radii of the circle centered at point A, and therefore that ADEC formed a parallelogram. When that thought occurred to me, I looked at the answers and saw that’s what the first two options combined indicated so it made sense to me that they were the correct answers which turned out to be correct. Boom. 🧨

I finished the first exercise of the two exercises I did this week Wednesday on my first attempt. It wasn’t too difficult, but there were some parts I found confusing and had to guess on. Below are three questions from that exercise:

Exercise 1 – Prove Triangle Similarity

Question 6

This question wasn’t difficult to understand, but my answers to the fill-in-the-blanks were still guesses because even though intuitively I understood what was going on, I wasn’t 100% sure what the correct terminology to use was. But nonetheless, I still got it correct.

Question 7

This was blatantly obvious by just filling in the values of each line segment and seeing that the equation wasn’t equal. I’m actually not sure why I bothered screenshotting it… 🤔

Question 8

This question was much more confusing than the others. It was pretty obvious to me that the first and third multiple choice options were both incorrect, but I couldn’t decide between the second and fourth options. Now the answer seems obvious, but at the time I was getting tripped up thinking that she didn’t prove that ∠F could be used for both triangles given that the triangles were flipped and dilated versions of each other. My gut told me the correct solution was the fourth option though, So I went with it and realized afterwards that the reason why it was the correct choice was because the letters denoting each triangle were not written in similar order. Again, now it seems blatantly obvious but at the time I was very confused. 

Exercise 2 – Prove Theorems Using Similarity

I started this exercise on Thursday and got through it on my first attempt. The questions were a bit harder for me than in the previous exercise but not too bad, overall. Here are two examples:

Question 9

I would have gotten the first fill-in-the-blank wrong here if I hadn’t looked at Part B which was congruent to Part A. (See what I did there? 😏) I wasn’t sure what the “reflexive property” was but went with it and it turned out to be correct. (FYI, it just means that something is the same thing as itself, so the angle ∠OMN is the same thing as the angle ∠PMO… Duh.)

Question 10

This was one of the more wordy and confusing questions I worked through this week. I got thrown off by all the letters denoting each line segment and it took me about 10 minutes to think through what the proof was saying. I eventually figured out exactly what it was saying, however, and was more-or-less confident when I submitted my answer.

Unit 4 – Similarity – Unit Test

I started this unit test on Friday and made it through the first seven of ten questions without making a mistake, but then decided to call it a day. I got back to it Saturday morning and got the final three questions correct, finishing off the test pretty easily. There were some tricky questions, but I only took screenshots one of the one below because at that point I was already up to ten questions for this post and didn’t want to have it be too long, plus a lot of the questions were similar to all the others ones I’ve answered over the past few weeks so it didn’t seem necessary. Anyways, here’s the one question I took screenshots of:

Question 11

I found this question quite hard. I tried to ‘cheat’ and use trig functions to answer it, and I think I probably could have, but I eventually realized trying to solve it that way wasn’t as easy as I thought it would be and I was sure there another approach that I wasn’t understanding. I realized that the angle on the left was the same as one of the two angles at the bottom of the triangle, and after that I used some algebra to figure out the hypotenuse and opposite sides of the other triangles, and with it the entire perimeter of the whole triangle.

So like I said, all in all it was a pretty good week for once! I’m now 91% of the way through Geometry which I’m happy about. What I’m really happy about though is that the next unit is titled Right Triangles and Trigonometry which hopefully will be more equation- and math-based and not as terminology-based as the past few units/exercises. 🥵There are three exercises I need to get through before I can start the unit test, so I’m hoping they won’t be too difficult. If that’s the case, then I’m also hoping I can get through the following unit this week as well, Analytic Geometry, which only has one exercise I need to do before I can redo its unit test. As always, my fingers crossed I can make some decent progress this week! 🤞🏼