Don’t let geometry define you

The "Given" is essential in geometry and in life

We’ve had more than one child struggle with geometry. Even Bryan, our son who ended up majoring in math, recently admitted at his college graduation that he was “not a geometry guy.” Along with many others in high school, he had a tough time grasping the spatial relationships of points, lines, angles, and figures. 

“I don’t want to major in triangles!” complained another smart but disgruntled guy who joined the ranks of those forced to face the world of geometry. Like Alice arriving in Wonderland, many frustrated teenagers often find themselves puzzled and bewildered by unfamiliar rules and strange new ways of looking at circles and other once-ordinary objects.

Although many have issued a resounding “Goodbye and good riddance!” at the end of taking the class, some of the smartest people I know have muddled through geometry. As a matter of fact, one such friend managed to get an almost perfect score on the math section of the SAT. Another, my sister, is one of the brightest, most well-read people I know. She can't remember any corollaries or theorems, but she can recall names and motives of minor Shakespeare characters; she may not be able to recite the formula for calculating the area of a circle, but she can casually take in an article from The Economist or The New Yorker while simultaneously contributing to a complex political discussion. No, geometry was not her forte. However, unlike many students, she managed to find a life lesson in high-school geometry: the principle of the “Given.”

Every proof in geometry provides some initial information, some facts are known as the “Given.” Using these pieces of evidence, we're required to complete the proof by creating a series of logically deduced statements. Coming from the same “Given” is essential not only when we solve geometry proofs but also when we participate in real-life deliberations. In other words, as my sister realized, when two people can’t agree on something, it’s often because they don’t come from the same “Given.”

I've seen this less conventional application of geometry bear itself out many times. For example, before serving a mission for my church, I had a friend warn me that I would not have much success teaching people if, together, we didn’t first agree about the nature of God. That is, if we didn’t come from the same “Given,” I would have very little chance of teaching what I considered additional truths. He was right. You can’t, for instance, convince a Buddhist to be baptized if he doesn’t first believe Jesus Christ is the Savior. 

Similarly, I’ve found it's tough to persuade my children to do their homework if, at the outset, we can’t agree that lifelong learning is up to them and that future opportunities depend on how well they perform in school today. In other words, it does little good to beat the drum with my conclusion if we can’t all hear the same prelude music.

Geometry is certainly not for everyone, but, for some reason, it's required for every high school student. So, although our final performance in the class should not define us, geometry principles can help shape our conversations. Furthermore, we can all agree to look beyond circles and triangles for larger life lessons. In fact, that’s a given.