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You’ve probably heard that geometry can be hard. In fact, you might even have believed it yourself. But whether you like it or not, geometry has always been part of the standardized tests you’ve taken and will continue to be until at least high school graduation. So, if you want to make sure that this doesn’t derail your entire academic career, don’t hesitate to ask for help when you need it most. Here are some tips on how to ace your geometry homework!
The Geometry Dissection Tool
One of my favorite tools for helping students build a solid conceptual foundation is called The Dissection Tool. Basically, it’s a way to help you work with shapes and their parts in a consistent and constructive way. First off, we’ll give you a more detailed look at how it works. Then, we’ll show you how and why you should use it when doing geometry homework help. Lastly, we’ll tell you why and how it can be used even beyond homework assignments. If your child is struggling with geometry (or any high-school or college course for that matter) don’t hesitate to reach out for some math tutoring. You’re never too old for homework help!
Proofs, Postulates and Theorems
Before you even think about picking up a calculator for geometry homework, you need to thoroughly understand proofs, postulates and theorems. Not sure what these terms mean? Don’t worry, you aren’t alone! These are three different types of statements that mathematicians use when discussing geometry. A proof is used to demonstrate whether or not a statement is true; it takes as its basis one or more assumptions that are believed to be true (aka hypotheses) and deduces logically from those statements other statements that must also be true (aka conclusions). A postulate is similar except it has no underlying assumptions; instead, it simply asserts something without explanation. Last but not least, a theorem is a statement whose truth has been demonstrated with certainty by rigorous logic and mathematics.
Isosceles Trapezoid
A regular trapezoid has two sides of equal length. An isosceles trapezoid, however, has at least two sides that are congruent and of different lengths. Consider an isosceles trapezoid ABCD. Since AB and DC are both congruent to AC, angle BDC = angle DBC = angle CBD.
Right Triangles
Take geometry, for example. A right triangle has a set of special properties that make it much easier to solve for its missing pieces than any other shape—it’s sort of like magic. For example, if you know two sides and one angle (otherwise known as a trigonometric identity), there’s a way to use that knowledge to find another side of your triangle. If you have no idea what I just said, don’t worry. That’s where we come in with our step-by-step guide on how to ace your homework.
Rhombuses and Rectangles
Rhombuses are most easily distinguished from rectangles by their diagonals, which are perpendicular to one another. These lines make it easy to figure out if a parallelogram is indeed a rhombus. To find out, locate each diagonal and then draw a line connecting them. If these lines form right angles with one another, you know that your parallelogram is in fact a rhombus. For example, here’s how two of its diagonals would look ____ ____ . Notice how they intersect at 90-degree angles? That means we can conclude that our parallelogram is indeed a rhombus. But what about triangles? Triangles have three sides—but not all three sides need to be equal for it to qualify as a triangle. The only thing that matters for something to be considered a triangle is that it has three sides. So even though there are many shapes with three sides, such as an equilateral triangle (where all three sides are equal) or an obtuse triangle (where one side is greater than another), they don’t qualify because they don’t have all three of their sides equal.
