Drawing triangles with given conditions and the triangle inequality theorem (7th grade math)

In each triangle, there are six basic pieces of information: the three side lengths and the three angle measures. But do we need ALL of those in order to be able to draw the triangle (and it be unique)? We start exploring this question in this lesson (and we continue in part 2). In this part, we especially focus on whether three given sides make a triangle, and on the triangle inequality theorem.

The triangle inequality theorem sounds fancy but it's a simple principle that you've already used in real life! If you need to travel from point A to point B, which is shorter, to go directly from A to B, or to first go from A to X, and then from X to B?

If I'm given three angle measures, and use those to draw a triangle, will the triangle be unique, or are there several different non-congruent triangles I could draw with that information?

What about if I'm given two angles and a side between them?
What about if I'm given two side lengths and an angle between them?
What if I'm given three side lengths?

Which conditions define a unique triangle, and which don't? There's a lot to this question and we don't go through every possible scenario in this video. Sometimes you get a unique triangle and sometimes not.

See also

Drawing Shapes

Math Mammoth Geometry 3 — a self-teaching worktext with explanations & exercises (grade 7)

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