Congruent Parallelograms?

Although you may not be able to tell by the picture, these blue and yellow parallelograms are the tops of two led containers for my mechanical pencil. I traced them with help from the construct>parallel line, construct>perpendicular line, and construct>midpoint tools in The Geometer's Sketchpad.
I drew two altitudes (k and n) in order to find the height of each parallelogram. Then, I multiplied each height by its corresponding base and, to my surprise, found these parallelograms to not have equal areas, and therefore not be congruent.
The total area of parallelogram ACDF is 17.16 square centimeters.
(~GC2)

Congruent Tangents

GC2

Tangents to a circle from a point are congruent. (Corollary)

I brought my camera to an ice cream parlor last week in hopes of finding an example of the corollary stated above. According to this corollary, tangents to a circle from a point are congruent. I found my ice cream cone to be a great example of this. In the picture, segments AB and AC are both tangent to the circle (scoop) at points B and C. This should assure that tangent AB is congruent to tangent AC, which was further proven when I measured the segments using GSP. 

Congruent Squares

These squares are congruent.  You can tell because they have parallel lines which are cut by a transversal. It follows that the interior angles are congruent.  It also shows that the same-side interior angles are supplementary.  This is obvious to see because a square has four 90 degree angles.  The squares also share a side and the same parallel lines. In conclusion, these two squares are congruent. (~KM5)

Carpeted Rectangles

Earlier today, I was looking at the carpet on my living room floor and I saw what appeared to be three similar quadrilaterals, more specifically rectangles.

I then took a picture of it and uploaded it to sketchpad to prove Theorem 5-12, which states that the diagonals of a rectangle are congruent. I measured the lengths and proved that it was a rectangle and then proved that the diagonals were congruent.

(~WM5)

Geometric Window

This is a picture I took of my garage window. I noticed more than one geometry concept in it. It is an example of parallel lines, congruent angles, and perpendicular lines. I compared the lengths of each segment with the length of my phone and they are indeed equal. -(CD1)

Triangle Tiles

These triangular tiles are displaying congruency and vertical angles. The triangles are isosceles because the two sides are congruent; the opposite angles are also congruent (Theorem 4-1). The triangles are all congruent by the SSS Postulate, because all three sides are congruent to three sides of another triangle. (~AV5)

PS4 Angles

I saw on my PS4 that front was made up of parallel lines, congruent angles and congruent shapes. To the left there are two congruent rectangles with lines on the top and bottom that are parallel to each other and same goes for the left side except the rectangles are bigger. (~DF5)

Geometric Tiles

  

Tiles are often used for flooring because of the intricate patterns and tessellations that they can form. In this photo you can see examples of congruent triangles. You can tell that they are congruent because of the verticals angles and the fact that they are next to squares -- this arrangement shows the use of the SAS postulate to prove the triangles congruent. You could also use parallel lines and interior angles to use the ASA postulate. (~AL1)