Learn at Mathematics Realm

Let us take note that the angles now of the triangle are angle 1, angle 2 and angle 3.

Since we have drawn a line parallel to line AC, then we could say that side AB and side side BC are transversals of the parallel lines BD and line AC. Let us recall the concept of alternating interior angles for parallel lines.

Since we know that these alternate interior angles are always equal, then in the figure that we have formed, angle 1 = angle 4 and angle 3 = angle 5.
If you notice, angles 2, 4 and 5 form a straight line. Let us recall
That means the sum of angles 4, 2 and 5 is 180 degrees, because they form a straight line.
From the illustrations above, let us recall that angle 1 = angle 4 and angle 3 = angle 5.
Further, it means that the sum of angles 1, 2 and 3 is also 180 degrees.
Therefore, we can conclude that
You can also use the other sides of the triangle for the proof. The same process will be used in each of the cases.
Here is the summary of the proof in pdf form. You may download and print for academic use. Hope it will become useful to you.
You comments ad suggestions are welcome here. Write them down in the comment box below. Thank you!

PROCEDURES:

3. Using a pair of scissors or cutter, cut the sector/region of the angles of each triangle.
4. For each of the triangles, arrange the regions of the angles in such a way that they are adjacent to each other. Notice that in this case, the lower part of the angles form a straight line.

5. In each of the figures formed, the angles formed a straight line at the bottom part. Recall that the sum of the angles that form a straight line is 180 degrees.

CONCLUSION: The sum of the measures of the angles of any triangle is 180 degrees.

For educators and parents, I have made a worksheet for this activity for your class/children. You are free to download and print it. You may group your students and let each group work on a triangle or all the triangles. I hope this will be helpful.

The right side has a common factor, which is 2. Using distributive property, it can be rewritten as  








If you notice, both sides has a common factor, which is b - a. To simplify the equation, let us divide both sides by the common factor.

The process will arrive at








Are you convinced? No no no...

Seems like the proof is valid but there is something wrong with it. Look over the proof once again. Can you identify which of the process is not valid?

There is nothing wrong with the given. Real numbers can be equal. There is nothing wrong also with adding b and subtracting 2a on both sides. Likewise, there is nothing wrong with combining like terms on both sides. Then, where is the mistake?

There is nothing wrong with dividing both sides by any number but in this case it becomes invalid. The reason is that b - a = 0 since a = b. Subtracting equal numbers will yield 0. Since b - a = 0, then the result will be UNDEFINED. We cannot also cancel out b - a on both sides because of that. 

Therefore, 1 is not equal to 2.  

Here is a copy of the proof in pdf form. You may download and print it for educational purposes.    You may share it to your friends. Your comments and suggestions are also welcome here. 

The letters of the Greek alphabet is commonly used to represent variables, constants, functions and more. They are used in different areas of mathematics and sciences. Here is a downloadable copy of the Greek alphabet.
  

Here are the variations of the DAMATH board available for download. You may choose which one is applicable for your class/school.

This is the second version of the downloadable graphing paper that can be used for math and science classes. The size of this grid paper is a4 (8.27in. x 11.69 in or 210mm x 297 mm). You may directly print it also.

You are also free to write your comments and suggestions about this below (using the comment box). Thank you!

This is one of the useful materials in Mathematics - the graphing paper or grid paper. The following graphing paper is designed for classroom use. It may be used not only for mathematics subjects but also for science subjects like Physics.

This is a graphing paper in letter size (8.5 in. x 11 in.). You can download this pdf file using the download arrow below. You can directly print it also.

I hope this may help you in any way. If there are any suggestions or comments about this graphing paper, please inform me through the comment box below. Thank you!