Math  /  Geometry

QuestionWhich set of side lengths represents a triangle with 3 lines of reflectional symmetry? 3,4,5 3, 6, 9 5, 5, 5 5,10,55,10,5

Studdy Solution

STEP 1

1. A triangle with 3 lines of reflectional symmetry is an equilateral triangle.
2. An equilateral triangle has all three sides of equal length.
3. We need to identify which set of side lengths represents an equilateral triangle.

STEP 2

1. Understand the properties of a triangle with 3 lines of reflectional symmetry.
2. Evaluate each set of side lengths to determine if it forms an equilateral triangle.
3. Identify the set that represents an equilateral triangle.

STEP 3

A triangle with 3 lines of reflectional symmetry is an equilateral triangle. This means all three sides are of equal length.

STEP 4

Evaluate each set of side lengths:
- Set 1: 3,4,53, 4, 5 - Set 2: 3,6,93, 6, 9 - Set 3: 5,5,55, 5, 5 - Set 4: 5,10,55, 10, 5
Check if all sides in each set are equal.

STEP 5

- Set 1: 3,4,53, 4, 5 - The sides are not equal. - Set 2: 3,6,93, 6, 9 - The sides are not equal. - Set 3: 5,5,55, 5, 5 - All sides are equal. - Set 4: 5,10,55, 10, 5 - The sides are not equal.

STEP 6

The set of side lengths that represents an equilateral triangle, and thus has 3 lines of reflectional symmetry, is:
5,5,5 5, 5, 5
The set of side lengths representing a triangle with 3 lines of reflectional symmetry is:
5,5,5 \boxed{5, 5, 5}

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