Three sides settle it
A metal shop joins three rods into a triangle. The shop measures no angle.
Slide the third rod. An arc is part of a circle. Watch whether the arcs cross.
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- The base: 68 mm.
- A 39 mm arc, swung from the left end.
- A 52 mm arc, swung from the right end.
- The arcs cross. That is the third corner.
Three sides fix a triangle
To fix a triangle is to allow only one shape and size. Draw the base. Draw one arc from each end with a compass. The arcs cross at the third corner. Full circles from the two ends cross in two places. The other crossing gives a mirror twin, a flipped triangle. That twin is congruent too.
SSS: two triangles have three equal pairs of sides. Then they are congruent. S stands for side.
Sides that fit on each other are corresponding sides.
Example: sides 52, 39 and 68 mm. Any triangle with these sides has corners of 34.8°, 49.6° and 95.6°.
Watch out!
Rods of 20, 20 and 68 mm make no triangle. The two short rods must add to more than the long one. Here 20 + 20 = 40, and 40 is less than 68.