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 ) .

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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
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**SSS Construction of Δ **

Construct ΔABC in which AB = 4.5 cm, BC = 5 cm and CD = 6cm.

- Draw a line BC of length 5 cm.

- From B, point A is at a distance of 4.5 cm. So, with B as center, draw an arc of radius 4.5 cm.

- From C, point A is at a distance of 6 cm. So, with C as center, draw an arc of radius 6 cm.

- A 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 A. Join AB and AC. ΔABC is the required triangle as shown in the figure.