In this video segment adapted from ZOOM, the cast tries to design …
In this video segment adapted from ZOOM, the cast tries to design and build a bridge made out of drinking straws that will support the weight of 200 pennies.
The precursors to what we study today as Trigonometry had their origin …
The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.
The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of …
The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.
The two triangles in this problem share a side so that only …
The two triangles in this problem share a side so that only one rigid transformation is required to exhibit the congruence between them. In general more transformations are required and the "Why does SSS work?'' and "Why does SAS work?'' problems show how this works.
For these particular triangles, three reflections were necessary to express how to …
For these particular triangles, three reflections were necessary to express how to move from ABC to DEF. Sometimes, however, one reflection or two reflections will suffice. Since any rigid motion will take triangle ABC to a congruent triangle DEF, this shows the remarkable fact that any rigid motion of the plane can be expressed as one reflection, a composition of two reflections, or a composition of three reflections.
This particular sequence of transformations which exhibits a congruency between triangles ABC …
This particular sequence of transformations which exhibits a congruency between triangles ABC and DEF used one translation, one rotation, and one reflection. There are many other ways in which to exhibit the congruency and students and teachers are encouraged to explore the different possibilities.
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