Not sure about MCC9-12.G.SRT.5 and others

[kpillow]

I’m a high school teacher in Georgia, and I teach a course called Coordinate Algebra. Many of the standards leave me wondering what it is I should do to convey a particular standard; they seem vague. For example,

MCC9-12.G.SRT.5 Use congruence and similarity criteria for triangles to
solve problems and to prove relationships in geometric figures.

While I do appreciate some freedom in which to work, my knowing what the
students will be responsible for knowing can be considered important. In other words, what relationships? One way I interpret this standard is that a student would be given a random relationship and asked to use his knowledge to prove that relationship.

Can you clear up my confusion over the “versatility” of the
standards? Am I looking at this too closely or not close enough? Thanks.

[Bill McCallum]

First, this standard is not necessarily about coordinate algebra at all. It is more about using the basic similarity and congruence criteria to solve problems with more complex figures. A simple example might be showing that the diagonals of a parallelogram bisect each other. Using this diagram, randomly chosen from the internet

one might first observe that $\mathrm{△}AOE$ is similar to $\mathrm{△}COB$, using the AAA criterion, and then use the congruence of opposite sides (previously proven) to conclude that the two triangles are congruent, and hence that $AO=OC$ and $BO=OD$. Of course, one can condense this argument with a direct appeal to the ASA criterion for congruence, but I quite like breaking it apart this way in this case, since the similarity is what first arises from the basic properties of transversals, and then the congruence depends on a previously established result.

Here is another very nice example, more complicated. It is a good example of looking for and making use of structure, because if you draw auxiliary lines parallel to the sides through E and F you see all sorts of similar triangles and can chain the ratios between them to solve the problem (I won’t spoil it for you by giving the solution).

I realize this doesn’t really give you the guidance you are asking for, but perhaps it will set some ideas in motion for the geometry course.

• This reply was modified 11 years, 7 months ago by Bill McCallum.

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