Question

which set of side lengths represents a triangle with 3 lines of reflectional symmetry?
3, 4, 5
3, 6, 9
5, 5, 5
5, 10, 5

Explanation:

Step1: Recall triangle properties

A triangle with 3 lines of reflectional symmetry is an equilateral triangle. In an equilateral triangle, all side - lengths are equal.

Step2: Check each option

• For the set \(3,4,5\): \(3

eq4
eq5\), so it is a scalene triangle (no lines of reflectional symmetry based on side - length equality).

• For the set \(3,6,9\): \(3 + 6=9\), which does not satisfy the triangle inequality theorem (\(a + b>c\) for a triangle with side lengths \(a,b,c\)).
• For the set \(5,5,5\): All side lengths are equal. An equilateral triangle has 3 lines of reflectional symmetry (one through each vertex and the mid - point of the opposite side).
• For the set \(5,10,5\): \(5 + 5<10\), which does not satisfy the triangle inequality theorem.

Answer:

\(5,5,5\)