You can only draw one unique isosceles triangle that contains an angle of 75 Which statement is true? A.Lara is correct, because only one unique triangle can be drawn the the given information B.Lara is incorrect, because the triangle described cannot be drawn with the given information C.Lara is incorrect because more than one triangle can be drawn with the given information D.None of the above

C. Lara is incorrect because more than one triangle can be drawn with the given information.

An isosceles triangle is defined as a triangle with at least two sides of equal length. When given an angle of 75 degrees, one can assume that it is either the vertex angle (the angle between the two equal sides) or one of the base angles (the angles opposite the equal sides).

If the 75-degree angle is the vertex angle, then the base angles must each be (180 - 75)/2 = 52.5 degrees. This scenario defines one unique isosceles triangle.

However, if the 75-degree angle is one of the base angles, then the vertex angle will be 180 - 2(75) = 30 degrees. It's also possible to have isosceles triangles with the 75-degree angle as a base angle and different lengths for the sides that enclose this angle, as long as the sides are equal; the vertex angle always ends up being 30 degrees in such a case, but the side lengths can vary.

Given only one angle of 75 degrees, there are actually an infinite number of isosceles triangles that can be drawn because the length of the sides isn't specified. Each different side length (while keeping the triangle isosceles) would result in a different unique isosceles triangle with the same angles but different overall dimensions - hence more than one triangle can be drawn with the given information.

Extra: Understanding isosceles triangles is foundational in geometry. An isosceles triangle has several important properties:

1. At least two sides have equal length (the legs). 2. The angles opposite those sides are also equal. 3. If only one angle is known in an isosceles triangle, it isn't enough to define a unique triangle without additional information, such as the length of the sides or another angle. 4. The altitude drawn from the vertex angle to the base not only bisects the vertex angle but also bisects the base into two equal segments and makes two congruent right-angled triangles.

When one works with isosceles triangles, it's important to remember that it's the combination of side lengths and angles that ultimately define a unique triangle, according to the law of congruence. The problem statement given provides insufficient information to draw one unique isosceles triangle, as it doesn't specify whether the 75-degree angle is the vertex angle or the base angle, nor does it give any information about the side lengths.