Question

what construction method creates the foundation for proving base angle congruence in isosceles triangles? (1 point)
drawing perpendicular lines to the base
constructing an angle bisector through the vertex
extending triangle sides symmetrically
connecting midpoints of triangle sides

Explanation:

When an angle - bisector is constructed through the vertex of an isosceles triangle, it divides the triangle into two congruent triangles (by Side - Angle - Side (SAS) congruence criterion since the two equal sides of the isosceles triangle are equal, the angle bisector creates equal angles at the vertex, and the common side is shared). From the congruence of these two triangles, we can prove that the base angles are congruent.

Answer:

B. Constructing an angle bisector through the vertex