If two sides of a triangle have the same lengths as two sides of another triangle, and one angle of the first triangle has the same measure as one angle of the second triangle, what can be said about them? Under what circumstances will they be congruent to one another?

Pose these problems to the Senior School students...

In this edition of ‘Adventures’ we study a few miscellaneous problems, mostly from the Pre-Regional Mathematics Olympiad (PRMO; this year’s PRMO was conducted on August 19 in centres all over the country). As usual, we pose the problems first and present solutions later.

The triangle inequality has a familiar cadence to it and most students can recite it spontaneously. In this article, we mathematise our understanding of possible triangle shapes, using the limits of values which the angles first, and then the sides, take. It's a great way for students to explore different ways of expressing their conceptual understanding.

Here is a more analytic & systematic way of counting the triangles puzzle. Sundarraman shares his solution.

Triangle ABC has A = 130 ◦ , B = 30 ◦ and C = 20 ◦ . Point P is located within the triangle by drawing rays from B and C, such that PBC = 10 ◦ and PCB = 10 ◦ . Segment PA is drawn. Find the measure of PAC.

In the previous issue of At Right Angles, we studied a geometrical problem concerning the triangle with angles of 130 ◦ , 20 ◦ and 30 ◦ . We made the comment that the problem belongs to a class of geometrical problems dealing with triangles with numerous lines drawn within them, intersecting at angles whose measures are an integer number of degrees; we are required to find the measure of some indicated angle. In this note, we study another problem of this genre—a particularly famous such problem.

Shailesh Shirali takes you to a wonderful tale of Pythagoren triples one more time.

How do we construct different types of triangles using scale and compass? This has been explained in a very simple manner in the presentation given below. 

Here is a compilation of the presentations that will come handy for the workshop.

These are developed at Shikshamitra.


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