Geometry

Question Analysis：
This question involves the concept of triangle construction based on side lengths.
The main focus is to determine whether a triangle with given side lengths can be uniquely constructed.

Key Concept Explanation：
The Side - Side - Side (SSS) congruence criterion states that if the lengths of the three sides of one triangle are equal to the lengths of the three corresponding sides of another triangle, then the two triangles are congruent.
In the context of triangle construction, when three side lengths are provided, and they satisfy the triangle inequality theorem (the sum of the lengths of any two sides of a triangle must be greater than the length of the third side), a unique triangle can be constructed.

Step - by - Step Solution：
First, check the triangle inequality theorem for the side lengths 5, 12, and 13.
Calculate 5 + 12 = 17, and 17 > 13.
Calculate 5+13 = 18, and 18 > 12.
Calculate 12 + 13 = 25, and 25 > 5.
Since the sum of the lengths of any two sides is greater than the length of the third side, these side lengths can form a triangle.
According to the SSS criterion, when three side lengths are given and they can form a triangle, a unique triangle can be constructed.

Option Analysis：
A) "No, because angles are needed" is incorrect.
With the given side lengths that satisfy the triangle - inequality theorem, a unique triangle can be constructed without additional angle information based on the SSS criterion.
B) "Yes, because it satisfies SSS" is correct.
The side lengths 5, 12, and 13 satisfy the triangle - inequality theorem, and by the SSS criterion, a unique triangle can be constructed.
C) "Only if it is right - angled" is incorrect.
The fact that the triangle with sides 5, 12, and 13 i...