Proof Without Words: If x >0, x + 1/x >=2

A picture is worth a thousand words, even in mathematics. Most of the time, complicated algebraic statements can be shown using geometric representations. One example is the sum of

\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots

which when added equals 1.

In this post, we show another geometric proof without words. Proof without words is not a proof per se but rather a representation that will help readers understand the proof.  » Read more

Why the Area of a Rhombus is Half the Product of its Diagonals

A rhombus is a parallelogram with four congruent sides. Since it is a parallelogram, it has also all the properties of a parallelogram. One of these properties is that the diagonals bisect each other. That is, they divide each other into two equal parts.

Another property of a rhombus is that the diagonals are perpendicular. So, summarizing all the properties above, if we have rhombus ABCD, then,

\overline{AB} \cong \overline{BC} \cong \overline{CD} \cong \overline{DA}.

and

\overline{AC} \perp \overline{BD}. » Read more

Explore Solid Nets Apps and Print Models

Are you looking for solid nets resources, printable worksheets, or interactive apps? Check out the five websites below. These sites contains resources about solids, their properties, and their nets. Printable nets are also available.

Annenberg Media has an interactive page on Platonic solids, prisms, and pyramids. It allows users to rotate 3d shapes and see how the solids are formed from their nets.

Illuminations has a page that lets you explore nets of Platonic solids. What is good about this interactive program is that it also allows you to create your own net.

Math Interactives  allows users to explore the relationship between the volume of the solids and their nets. Users can also check if their visualization skill by predicting the top view, front view, and side view of the solids.

solid nets

Maths is Fun – Maths is fun has a page about Platonic solids. The resource includes properties, printable nets, as well as 3d interactive animations.

SEN Teacher is a website that provides free learning materials. The website has free printable nets of polyhedra which is available in PDF. The website also allows users to create  customize nets putting images on them creating “photonets.”

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