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 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.

Answer 1

lol lol lol. 1st draw this out.
1. should be the  asa tct because there is 1 side that is given that is equal(ad and cd, but it could also be bd, but idk if you learned that yet) , and 2 angles are given that are equal (bda and bdc, bac, acb)
2)CPCTC (congruent parts of congruent triangles are congruent.

Answer 2

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