Understanding Point Symmetry

In the previous post, we have learned about line symmetry. In this post, we are going to learn about point symmetry, another type of symmetry.

If a figure is rotated 180 degrees about a point and it coincides with its original position, then it is said that the figure has point symmetry. The point of rotation is called the point of symmetry.

The figure below shows the point symmetric polygon ABCDEF rotated clockwise about P, its point of symmetry. The polygon outlined by the dashed line segments shows its original position.  » Read more

Properties of Similar Triangles Part 1

This is the second part of the Triangle Similarity Series.  The first part is Introduction to Similarity.

In Introduction to Similarity, we have learned that similar objects have the same shape, but not necessarily have the same size. We drew a triangle using a graphics software zoomed it in and zoomed it out producing similar triangles.

Are Buu and Patrick 'similar'?

Zooming did not change the shape of the object. In effect, the measure of the interior angles of a triangle did not change.  » Read more

Corresponding Angles of Similar Objects

In this post, one property of similar objects. In the previous article, we have discussed that if we want to preserve the appearance of our picture or object (that is without being stretched), we will have to enlarge or reduce it with the same proportion. That means that if we double the width of our picture, then we will also have to double the length.  We have done this using the two triangles as shown below.  We made sure that if we pair the sides of the two triangles, in each pair, the length of the side of the larger triangle is always twice the length of its pair.  This means that the length of DF is twice the length AC, the length of DE is twice AB, and the length of EF is twice the length of BC.

» Read more

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