which set of side lengths represents a triangle with 3 lines of reflectional symmetry?\n3, 4, 5\n3, 6, 9\n5…

Explanation:

Step1: Recall triangle - symmetry property

An equilateral triangle has 3 lines of reflectional symmetry and in an equilateral triangle, all side - lengths are equal.

Step2: Check each option

• Option 1: 3, 4, 5 is a right - triangle (by the Pythagorean theorem (3^{2}+4^{2}=5^{2})), not equilateral.
• Option 2: Since (3 + 6=9), these side - lengths do not form a triangle (violates the triangle inequality theorem (a + b>c) for a triangle with side - lengths (a), (b), (c)).
• Option 3: 5, 5, 5 represents an equilateral triangle as all sides are equal.
• Option 4: Since (5+5 = 10), these side - lengths do not form a triangle (violates the triangle inequality theorem).

Answer:

5, 5, 5