It was another poor week for me on KA but, nonetheless, I’m surprisingly upbeat about how it went. I made it through two exercises but didn’t manage to get through the Congruence unit test—or even start it for that matter—which was part of my goal for this week. So, in that sense it was a bad week, especially considering that I thought my goal was relatively easy/reasonable. I got my ass kicked by the first exercise and didn’t think I was even going to pass it before the end of the week, but then the questions suddenly all became obvious to me on Saturday. After that, I finished the second exercise in about 15 minutes so even though the majority of the week was atrocious, I managed to finish the week on a high-ish note. 😮‍💨 The questions I worked through were once again all terminology-based where I had to choose/create the right sentences that described proofs for congruence. It was super frustrating. So ya, all in all, not a great week but progress nonetheless. 

The first exercise I worked through, Prove Parallelogram Properties, was all about proving congruence in parallelograms. Part of what made getting through this exercise difficult was that for some reason it had seven questions in it instead of the usual four, i.e. I had to get seven correct in a row which was challenging. At the beginning I was simply guessing what the solutions were and sometimes got them right. As the week went on, I slowly got a better grasp on the congruence criterion and eventually was able to reason my way through each question and properly figure out the solution. Here are six questions from the exercise:

Exercise 1 – Prove Parallelogram Properties

I didn’t know what I was doing trying to answer this question, but I thought through which notation referred to which triangle and determined the bottom two solution options would make the most sense since together they formed the rectangle. At that point, it just seemed to make sense to go with the side-angle-side criterion which turned out to be correct.

Question 2

The first solution to this question was obvious since it was a given on the diagram. At the time, I just guessed that the angles of ∠ABD and ∠CDB were congruent, but by the end of the week I could have told you that the reason why they’re congruent was because they’re the interior angles of a transversal (i.e. the diagonal line) that goes across two parallel lines.

Question 3

The note I wrote down for this question was, “again, no clue what was going on here.” I think I ended up getting it correct because I had gotten it wrong before and had just memorized the correct answers to put in. 🤷🏻‍♂️

Question 4

I answered this question on Saturday and it was the first question where I was able to think through what the correct solution was and felt confident that I was correct before answering it. It took me about five minutes to think through and I had to read the stages from top to bottom a few times before filling in the blanks. When I thought I had it figured out, I submitted my answer and got it right and was PUMPED.

Question 5

I thought about this question for a while and eventually concluded that the diagonal line was a transversal going across two sets of parallel lines, meaning that both sets of alternating interior angles would be congruent, and since each triangle shared the line AC, the triangles ΔABC and ΔCDA themselves would be congruent, and so the first solution would be correct. (I’m guessing that didn’t make sense…) After thinking through it for about five minutes, I also realized it was literally the same type of question as the previous one and that the same logic applied to both questions. 🙃

Question 6

This may have been the last question I answered to finish off the exercise and all I wrote in my notes was, “ [I] thought through this question fully and properly.” Boom. 🧨

I started this next exercise on Sunday and, as I mentioned, finished it on my first try. It was much easier than the first exercise which was a relief. Here are two questions from the exercise:

Exercise 2 – Justify Constructions

Question 7

The answer to this question seemed to obviously be the first option which was correct, but I was confused by the way the diagram was drawn. It didn’t seem obvious to me that where the ray CD started from was the centre of circle C. It must be implied but I wasn’t sure. Anyways, I went with the first option and, as you can see, got it correct.

Question 8

This question was just like the other three questions I worked through in the sense that I didn’t really know what I was doing/what was going on, BUT I was able to reason through it. It seemed clear that if line segments BE and BD were congruent and a part of the same line and line segments FE and FD (not shown) were congruent, the four lines together would create an isosceles triangle with line segment BF running straight down the centre. This would mean BF would have to be parallel to line segments BE and BD. Boom. Reasoned.

And that was it for this week. Like I said, I’m disappointed that I didn’t make it through the unit test but was honestly just relieved to have made it through that first exercise. 🥵 I tried a few questions on the unit test to see what they were like and, although I got one wrong (because I was rushing through it and didn’t think it through), they didn’t seem too difficult, so I’m hoping I can get through the unit test early this coming week. I’m also hoping that the next unit, Unit 4, Similarity, will be more ‘equation-based’ and not ‘terminology-based’, so to speak. There are only two exercises I need to do in that unit so, assuming I can get through the Congruence unit test quickly, I’m hoping to finish off both exercises AND the unit test before the end of the week. So as always, fingers crossed! 🤞🏼