Question

Given: Base ∠BAC and ∠ACB are congruent.
Prove: ΔABC is an isosceles triangle.
When completed (fill in the blanks), the following 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 _______1________.
Line segment AD is congruent to Line segment DC by _______2________.

Answer 1

the definition of congruent angles
Angle-Side-Angle (ASA) Postulate


the definition of congruent angles
the definition of a perpendicular bisector


Angle-Side-Angle (ASA) Postulate
the definition of a perpendicular bisector


Angle-Side-Angle (ASA) Postulate
corresponding parts of congruent triangles are congruent (CPCTC)