Questions: #13: Gerald thinks that isosceles triangles and equilateral triangles are not related because isosceles triangles have two sides that are the same length and equilateral triangles have three sides that are the same length. Is he correct? Explain.

Solution Steps

To determine if Gerald is correct, we need to analyze the definitions of isosceles and equilateral triangles. An isosceles triangle is defined as having at least two sides of equal length, while an equilateral triangle has all three sides of equal length. Since an equilateral triangle satisfies the condition of having at least two sides of equal length, it is a specific type of isosceles triangle. Therefore, Gerald is incorrect in thinking they are not related.

An isosceles triangle is defined as a triangle with at least two sides of equal length. An equilateral triangle is defined as a triangle where all three sides are equal in length.

Given the sides \( [3, 3, 3] \):

• To check if it is isosceles, we observe that at least two sides are equal: \( 3 = 3 \).
• To check if it is equilateral, we see that all three sides are equal: \( 3 = 3 = 3 \).

Since the triangle with sides \( [3, 3, 3] \) satisfies both conditions, we conclude:

• It is isosceles: \( \text{isosceles} = \text{True} \)
• It is equilateral: \( \text{equilateral} = \text{True} \)

Final Answer