Sydney Opera House

When I was in Sydney, Australia, I took a picture of the opera house and noticed that where the bottom of the arch touched its platform created a right angle with a point directly above it and the point on the end of the building. So, I figure that every arch of the opera house has a right triangle at the base of every one.(~MM2)

Similar Polygons

These two books (quadrilaterals) appear similar because their sides seem to be proportional. To verify, I measured the lengths: the larger book is 10 in x 6 in, and the smaller book is 6.5 in x 4 in. But 10:6 is NOT equal to 6.5:4, so in fact they aren't similar, as the sides are not proportional. (~KR2)

Changing Views

This is an example of a simple book which is meant to show that all real-life objects aren't perfectly geometrical. Although this appears rectangular, the book doesn't have exactly two sets of parallel lines and four right degree angles. The angles are slightly more or less than 90. However, you can see that numbers are very close to the theorems we have studied.

This picture is the same book at a different angle. You can see that front the top it appears to be a rectangle(above), but when it is taken from a slightly different angle things change. Due to perspective, the book looks a trapezoid. There is one set of parallel lines because angle FGJ and angle GJI are supplementary. The same thing applies with angle IFG and angle JIF. (~SV1)

Parallel Lines

This shows that angle ABC is congruent to angle ADE, and therefore segment BC is parallel to DE by postulate 11 -- it states that if corresponding angles are congruent when a transversal crosses two lines then those lines are parallel. (~JZ5)