Geometric Tiles

These tiles are an example of if two parallel lines are cut by a transversal, alternate interior angles are congruent. (~JZ5)

Parallel or Not?

By looking at this playground structure, I thought that these lines were parallel. Yet when I added the lines and points, I took the measurement of the two alternate interior angles, and found out that they were not congruent. It could be the angle that I took this picture that makes the lines not parallel, or the lines could be not parallel themselves. (~MM2)

Geometry From Mars

This is a picture from a Thirty Seconds to Mars concert. In the background, they have their logo, which is an example of an equilateral triangle and parallel lines cut by a transversal.

Equilateral Triangle:

Parallel Lines and Transversal:

Line FH is parallel to line EI and the transversals are AB and AC. This also demonstrates Theorem 3-2 (If two parallel lines are cut by a transversal, then alternate interior angles are congruent) and Theorem 3-3 (If two parallel lines are cut by a transversal, then same-side interior angles are supplementary) -- here [59.94 + 120.06 = 180; 60.59 + 119.41 = 180]. (~CS1)

Proving Lines Parallel

After a quick glance at my room, I noticed the overwhelming amount of parallel lines that could be found in my blinds. But, were these lines surely parallel?

We can prove lines parallel in various ways. According the Theorem 3-6, if two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel.

We can see in the above photo that this theorem has been proven. After adding in a transversal line, we can see that the same side interior angles, ∠1 and ∠2, are supplementary, therefore proving the lines must be parallel. (~RO5 )