If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
In an isosceles triangle, two sides have equal lengths, and consequently, two angles are also equal
In an isosceles triangle, two sides have equal lengths, and consequently, two angles are also equal. Let’s use this information to evaluate the statement options.
Option 1: Angle A is also 130°.
This statement cannot be true because in an isosceles triangle, the base angles (the angles opposite the equal sides) are equal, but they are not necessarily equal to the vertex angle.
Option 2: Angle A is 25°.
This statement cannot be true because in an isosceles triangle, the base angles are equal, meaning that if one base angle is 25°, the other base angle should also be 25°. However, the vertex angle being 130° means that the base angles are larger.
Option 3: Angle C is 25°.
This statement must be true. Since angles A and C are the base angles of the isosceles triangle, they are congruent. Therefore, if angle A is not 130°, it must be smaller. This means that angle C, being one of the base angles, should also be smaller. The only option provided that satisfies this condition is angle C being 25°.
Therefore, the correct statement is: Angle C is 25°.
More Answers:
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Understanding Triangle Properties | Triangle Inequality Theorem and Special Cases like Equilateral and Isosceles Triangles