The Construction of Triangle is controlled by the congruential theorems. For Construction of Δs one needs to know three values (either sides S or angles A): SSS, SAS, ASA and right triangle ( HL or RHS ) .
Note that it is not sufficient to know only three angles.
In order to be able to construct a Δ from three segments, one of the segments must be shorter than the sum of the other two: a < b+c, or b < a+c, or c < a+b
SSS Construction of Δ
Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6cm.
Step 1. Draw a line YZ of length 5 cm.
Step 2. From Y, point X is at a distance of 4.5 cm. So, with Y as center, draw an arc of radius 4.5 cm.
Step 3. From Z, point X is at a distance of 6 cm. So, with Z as center, draw an arc of radius 6 cm.
Step 4. X has to be on both the arcs drawn. So, it is the point of intersection of arcs. Mark the point of interaction of arcs as X. Join XY and XZ. ΔXYZ is the required triangle as shown in the figure.