Given: Base ∠BAC and ∠ACB are congruent. Prove: ΔABC is an isosceles triangle. When completed (fill in the blanks), the followin
g paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle. Construct a perpendicular bisector from point B to Line segment AC. Label the point of intersection between this perpendicular bisector and Line segment AC as point D: m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector. ∠BDA is congruent to ∠BDC by the _______________. Line segment AD is congruent to Line segment DC by _______________. ΔBAD is congruent to ΔBCD by the Angle-Side-Angle (ASA) Postulate. Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC). Consequently, ΔABC is isosceles by definition of an isosceles triangle.
