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 - side - length rule

For three side - lengths \(a\), \(b\), and \(c\) to form a triangle, \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check each option for triangle formation

• Option 1: \(3 + 4>5\), \(3+5 > 4\), \(4 + 5>3\), but it's a right - triangle with 1 line of symmetry.
• Option 2: \(3+6=9\), so it does not form a triangle.
• Option 3: \(5 + 5>5\), \(5+5 > 5\), \(5 + 5>5\). An equilateral triangle with side - lengths \(5,5,5\) has 3 lines of reflectional symmetry.
• Option 4: \(5+5 = 10\), so it does not form a triangle.

Answer:

C. 5, 5, 5