Home › Forums › Questions about the standards › 7–12 Geometry › Not sure about MCC9-12.G.SRT.5 and others
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August 9, 2013 at 8:25 am #2206kpillowMember
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.August 22, 2013 at 9:34 pm #2224Bill McCallumKeymasterFirst, 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 $\triangle AOE$ is similar to $\triangle COB$, 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 10 years, 8 months ago by Bill McCallum.
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