Question

With which 3 given elements we can’t construct unique triangle?

(a)AAA (b)SSS (c)SAS (d)ASA​

Answer 1

(a)AAA

Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles.

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Answer 2

With AAA, we can't construct a unique triangle.

Requirements for drawing a unique triangle :

• To construct a unique triangle, we need at least three measurements. (these measurements include angles, sides, etc.)

Why can't we draw a unique triangle with AAA data?

• Now, we know that the measurement of an angle doesn't depend upon the length of its two sides. The length of two sides of an angle can be increased or decreased to any desired extent while keeping the actual measurement of the angle, unaltered.
• So, if we have AAA data or measurements of three interior angles of a triangle, we cannot construct a unique triangle. Because, there will be uncertainty about the length of the sides of angles, which will eventually act as the uncertainty about the length of the sides of the triangle itself. That's why there can be infinite numbers of triangles with equal interior angles.

(On the other hand, we can draw unique triangles by using SSS, SAS, or ASA data. Because, in such cases, one or more sides are specified. So, the previous uncertainty about the length of sides will be eliminated.)

Hence, with AAA, we can't draw a unique triangle.