Monday I asked my students to determine whether this triangle was equilateral, isosceles, or scalene, and to prove their answer. The hint is in the post title: this is a Pythagorean Theorem activity. Here is the original triangle: If you said "isosceles," you're correct! Here's the proof, using Pythagoras's Theorem. The hypotenuse of the right triangle,... Continue Reading →

# Pythagorean Theorem Follow-Up

Activity for the big kids today: Without using a ruler, determine whether this triangle is equilateral, isosceles, or scalene. Prove it.

# Pythagorean Theorem

In over our heads with radicals in 8th grade Algebra this week, so we took some time to review the Pythagorean Theorem. Geometry is so beautifully concrete. In addition to demonstrations you can do with drawings and such, here's an example of a very cool model that my 8th graders found wonderfully entertaining. As... Continue Reading →

# Geometry in the Real World

Whenever I'm working on geometry with my students, I try to keep the focus as real-world as possible. So much of math operates in the abstract; geometry, by contrast, is thoroughly tangible. This is a time when we can easily and naturally give ideas to the hand before we give them to the mind. Take... Continue Reading →

# Geometry Across the Curriculum

I use geometric drawing across the curriculum in several projects. Below is an in-progress shot of an 8th-grader's design for a stained glass window, an assignment from my medieval history unit that incorporates symbolism along with geometric design. In world history, we use geometric drawing when studying Roman and Islamic mosaics, and students have the... Continue Reading →

# Construct a Hexagon

The construction for a regular hexagon is a favorite of my students every year and the one most of them choose as a basis for their geometric design project. We are simply going to begin with a line and use our compass to draw three congruent circles along it. Start with the center circle. Mark... Continue Reading →

# Construct a Square

This simple, elegant construction yields a square simply by using the steps to bisect a segment. Begin by using your compass to draw a circle, making sure to mark its center. With your straight edge, draw the diameter of the circle. This diameter is the segment you will bisect, which will produce a new segment... Continue Reading →

# Bisect an Angle

Today we'll be bisecting an angle, i.e. cutting an angle in half without using a protractor to measure. Begin with any angle and draw an arc from the vertex (V) such that your arc crosses both rays of the angle. Call the points where your arc crosses those rays points A and B. At this... Continue Reading →

# Bisect a Segment

Today we'll be doing a very simple construction -- bisecting a segment. In other words, we will be cutting a line segment in half. Begin by drawing matching circles from your two endpoints (A and B). The radius of the circle is not important. As long as it is more than half the length of... Continue Reading →

# Identify Geometric Shapes

Here's a little activity to wrap up our geometry study for the week. Have your students consider the following drawing and try to identify as many polygons as they can. If they need a little guidance, here are some possibilities... regular hexagons rectangles parallelograms rhombi other irregular quadrilaterals a multitude of triangles -- equilateral, isosceles,... Continue Reading →