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Construct a Triangle Given the Lengths of Its Three Sides - Constructing a Triangle When the Length of Its Sides Are Known (SSS Criterion)

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Constructing a Triangle When the Length of Its Sides Are Known (SSS Criterion):

We would construct triangles when all its sides are known. We draw first a rough sketch to give an idea of where the sides are and then begin by drawing any one of the three lines.

1) Construct a triangle ABC, given that AB = 5 cm, BC = 6 cm and AC = 7 cm.
 
Step 1: First, we draw a rough sketch with a given measure.
 
Step 2: Draw a line segment BC of length 6 cm.
 
Step 3: From B, point A is at a distance of 5 cm. So, with B as center, draw an arc of radius 5 cm.
Step 4: From C, point A is at a distance of 7 cm. So, with C as the centre, draw an arc of  radius 7 cm.
Step 5: A has to be on both the arcs drawn. So, it is the point of intersection of arcs. Mark the point of intersection of arcs as A. Join AB and AC. ∆ABC is now ready.
We observe that ∆DEF exactly coincides with ∆ABC.
 
Thus, if three sides of one triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent. This is SSS congruency rule.
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