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Could two followers please copy and re-post this tweet to show that someone is always there? Dial or text 988 (US National Suicide Lifeline). Just two. Any two. Copy, not retweet.

#math #geometry What fraction of the trapezoid’s area is shaded? What are the least and greatest values that fraction can take? What shape does the trapezoid become in each case?

#math #geometry Here's a rhombus. What kind of quadrilateral is shaded? Can you prove it? What fraction of the area is shaded? (Does the answer depend on just a and b?) What are the least and greatest values that fraction can take, and what shaded shapes go with them?

Here's a collection of proofs of the Pythagorean Theorem: geogebra.org/m/qyMFmVaS My questions to you: 1. Do you have a favorite proof in this book? 2. Do you have a favorite proof you'd like to see added to this book? 3. Some proofs are followed by Q&A. Do you find that useful?

With this applet, you compare two parallelograms. The purpose is to understand the A=bh area formula for a parallelogram. geogebra.org/m/ayrdu78p 1. Does the included Q&A make sense to you? 2. What question(s) would you finish with in order to bring home the punch line?

There are lots of ways to count on your fingers. Here's one system that essentially turns your hands into a two-bead abacus: you can use it to count to 99. As a math-positive adult, I use this system more than any other finger counting method. geogebra.org/m/sc7zd8bx

It's easy enough to slice a circular pizza into equal-area slices. Same for an annular pizza (circular, with a concentric circular hole). What about a circular pizza with an off-center circular hole in it? Try your hand: geogebra.org/m/gmgt4bqm

Why do the graphs of the secant and cosecant functions look the way they do? Why do rational functions often have vertical asymptotes? This applet lets you play with reciprocal graphs, drawn in real time, to develop some intuition about these things. geogebra.org/m/gac8qd8p