Question

Which of the following polygons are uniquely determined when all the sides are given?
A. Quadrilateral
B. Triangle
C. Pentagon
D. Hexagon

Answer 1

Hint-in this question, we need to know the basics of polygons. So that we apply this theory in this case. Like, A polygon having 3, 5 and 6 as its side is always a triangle, pentagon and hexagon respectively. But a polygon having 4 sides can be square, rectangle, parallelogram, rhombus and quadrilateral.

Complete step-by-step solution -
A polygon having 3, 5 and 6 as its side is always a triangle, pentagon and hexagon respectively. But a polygon having 4 sides can be square, rectangle, parallelogram, rhombus and quadrilateral.
SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Angle-side-angle is a rule used to prove whether a given set of triangles are congruent. The ASA rule states that. If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
Similarly, we also need to know about-
SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.
So, by analysis of above triangle congruence theorem
We conclude that,
Triangles are uniquely determined by specifying three sides (SSS Theorem) or by two angles and a side (AAS theorem) or by two sides and one angle (SAS theorem).
Therefore, option (B) is the correct answer.

Note- The Unique Shape Theorem states that all regular polygons with the same number of sides are similar to each other. And the immediate result of this theorem is that there is one unique shape for them.