High School

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Given ∆ABC,

1. If only one side of ∆ABC is given say 5.5cm, can you draw the exact copy of it? The answer is NO, because you can draw a number of triangles using two another arbitrary side as follows.

2. If only two sides of ∆ABC is given (say 5.5cm and 3.4cm) can you draw the exact copy of it? The answer is NO, because you can draw a number of triangles using the two sides and another arbitrary side as follows.

3. If all the three sides of ∆ABC is given (say BC= 5.5cm, AC= 3.4cm and AB=5cm) can you draw the exact copy of it? In this case you can draw a single triangle which is the exact copy of ∆ABC.

So, to draw an exact copy of ∆ABC, we need the length of three sides of the triangle. We call this side - side - side congruence criterion.

Answer :

This question is about understanding how to determine when a triangle can be exactly copied using different combinations of its side lengths. Let's go through each part step-by-step:

  1. One Side Given:

    • If only one side of a triangle is known, say 5.5 cm, it's impossible to draw a unique triangle. Although you can start by drawing a line segment of 5.5 cm, without any additional information, there are countless possibilities for the other two sides, resulting in infinitely many different triangles.

  2. Two Sides Given:

    • If two sides are known, such as 5.5 cm and 3.4 cm, drawing a unique triangle is still not possible. You can have an infinite number of triangles with different shapes by changing the angle between these two sides while maintaining their lengths. Without the third side or an angle, the triangle's shape is not fixed.

  3. Three Sides Given (SSS Criterion):

    • When all three sides of a triangle are known, for instance, BC = 5.5 cm, AC = 3.4 cm, and AB = 5 cm, you can draw exactly one unique triangle. This uses the Side-Side-Side (SSS) congruence criterion. According to this criterion, if three sides of one triangle are equal to three sides of another, the triangles are congruent (identical in shape and size).

In conclusion, to draw an exact copy of a triangle, the lengths of all three sides must be known. Only then can you use the SSS criterion to determine an exact copy of the triangle.

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Rewritten by : Barada