Base Angles
In geometry, the base angles of a triangle refer to the pair of angles that are formed by the base of the triangle and the two legs
In geometry, the base angles of a triangle refer to the pair of angles that are formed by the base of the triangle and the two legs. Specifically, the base angles are the two angles that are opposite to the two congruent sides of an isosceles triangle.
To understand this concept, let’s consider an isosceles triangle ABC. Assume that sides AB and AC are congruent, making angle A the vertex angle. Thus, angles B and C are the base angles.
One important property of base angles is that they are always equal in measure. This is a result of the fact that the two congruent sides of an isosceles triangle are of equal length. Consequently, the angles formed at the base will also be congruent.
To prove this, we can use the properties of triangles and angles. In triangle ABC, we know that the sum of the interior angles is 180 degrees. Thus, if angle A is equal to x degrees, then angles B and C will each be (180 – x)/2 degrees since the sum of angles B and C must be 180 – angle A.
Alternatively, we can use the concept of an isosceles triangle’s base angles theorem, which states that “if two sides of a triangle are congruent, then the opposite angles are congruent.” This theorem directly implies that in an isosceles triangle, the base angles are equal.
In summary, base angles are the pair of angles in an isosceles triangle that are formed by the base and the two congruent sides. They are always equal in measure and can be proven using the properties of triangles or the base angles theorem.
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