Question

when completed (fill in the bank), the following paragraph proves that AB is congruent to BC making ABC an isosceles triangle

Answer 1

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 definition of congruent angles.  

Line segment AD is congruent to Line segment DC by by the definition of a perpendicular bisector.  

ΔBAD is congruent to ΔBCD by the _______1________.  

Line segment AB is congruent to Line segment BC because _______2________.  

Consequently, ΔABC is isosceles by definition of an isosceles triangle.

corresponding parts of congruent triangles are congruent (CPCTC)

the definition of a perpendicular bisector

the definition of a perpendicular bisector

the definition of congruent angles

the definition of congruent angles

the definition of a perpendicular bisector

Angle-Side-Angle (ASA) Postulate

corresponding parts of congruent triangles are congruent (CPCTC)