Eikev- Congruence and Similarity

"When I ascended the mountain to receive the Tablets of stone, the Tablets of the covenant that Hashem sealed with you, and I stayed on the mountain for forty days and forty nights; bread I did not eat, and water I did not drink. And Hashem gave me the two stone Tablets, inscribed by the finger of Hashem, and on them were all the words that Hashem spoke with you on the mountain from the midst of the fire, on the day of the congregation." ~Devarim 9;9-10

Rashi on Devarim 9;10:
"Tablets"- It is written, i.e, spelled, but not vowelized, like the word לוחת (luchat), "tablet," in the singular, for both of them were equal.
In Tanchuma 10 it is explained that לוחות (luchot) is the full spelling. Here, however, the shorter spelling is used in order to indicate to us that the two tablets were actually identical in size and weight even though the first tablet had many more words carved into it than the second.

Congruence and Similarity:
congruence of shapes- in Geometry, two shapes are considered congruent if they are exactly the same size and can be shifted, turned, or flipped in such a way that one shape would fit perfectly on top of the other

similarity of shapes- in Geometry, two shapes are considered similar if they could be stretched or shrunk (maintaining all proportions) to fit on top of each other. If after adjusting the size, they need to be shifted, turned, or flipped in order to line up on top of each other, they are still considered similar.

While ratio calculations and comparisons for different shapes is learned in formal Geometry classes, congruence and similarity are basic concepts that students can start to investigate from early on in Elementary school. Students can play with shapes to see if it's possible to flip or turn them to fit on top of each other. Having hands-on manipulative pieces for students to explore with make it easier for younger kids to test out whether their theories of congruence and similarity between different shapes are accurate or not.

Parsha Connection:
In this week's parsha, Rashi together with the Tanchuma explain that one might assume that the two tablets were not the same in size and weight based on the fact that the first tablet had many more words carved into it than the second. We learn here, however, that despite the discrepancy in the number of words carved into each tablet, nevertheless, the size and weight of both tablets were equal. While weight does not factor into similarity or congruence, size and shape do. It is interesting that you might assume that with more words on the first tablet, maybe the tablets would have been similar- the same shape, but having the first larger than the second in order to fit all of the carvings. However, the tablets were not just similar, they were actually congruent- having the exact same size and shape, and they could have been placed to fit one exactly on top of the other, lined up perfectly with each other.

Everyday Connection:
Shapes are all around us. Have you ever noticed that when looking at a decorative wall, for example, some combinations of shapes are more appealing than others? It is natural for us to prefer combinations of shapes that include similar and congruent shapes, as they match well with each other. 

Have you ever looked at wainscoting on a wall and been bothered by one or two panels? If you look closely at the panels and measure them, you'll probably find that the proportions are slightly off, so even though they were meant to appear congruent, the measurements are actually off just enough that they are not, in fact, congruent or similar.

Does your personal design style tend more towards congruent and similar shapes or do you tend towards a more dynamic mix of different shapes? In trying to create dynamic designs, do you mix shapes or prefer to stick with the same shapes even if they are not congruent or similar to each other?