Concept explainers
To find: The reason for whether the isosceles

Answer to Problem 46HP
The reason for whether the isosceles triangle is always, sometimes or never the longest side of the triangle are described.
Explanation of Solution
Consider a triangle that has one side longer than the other side only when the
Consider the base angle that are less than 60, the vertex of such angle are of more than 60. In such case the base of the isosceles triangle is longest as shown in Figure 1
Figure 1
Consider the base angle that are equal to 60, the vertex of such angle are of equal to 60. In such case the triangle is equilateral as shown in Figure 2
Figure 2
Consider the case when the base angle measure is more than the vertex angle. In such case the base is not the longest side as shown in Figure 3
Figure 3
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