Question

1. what ensures a triangle constructed using the sss method is unique?

a. the inclusion of two equal angles
b. the presence of a right angle
c. the flexibility of side lengths
d. the fixed lengths of all three sides

Explanation:

The SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are equal in length to three sides of another triangle, the triangles are congruent (identical in shape and size). For a triangle constructed using the SSS method, the key factor that makes it unique is that all three side lengths are fixed.

• Option a: The SSS method does not involve angles, so the inclusion of two equal angles is not relevant.
• Option b: The presence of a right angle is related to right - angled triangles and the SSS method is a general triangle construction method that doesn't rely on a right angle for uniqueness.
• Option c: If side lengths were flexible, the triangle would not be unique.
• Option d: Since the lengths of all three sides are fixed in the SSS construction, this ensures that the triangle is unique.

Answer:

d. The fixed lengths of all three sides