Question

Given: Base ∠BAC and ∠ACB are congruent.

Answer 1

Refer to the image attached.

Given: $\angle BAC$ and $\angle ACB$ are congruent.

To Prove: $\Delta$ABC is an isosceles triangle.

Construction: Construct a perpendicular bisector from point B to Line segment AC.

Consider triangle ABD and BDC,

$\angle BAD = \angle BCD$ (given)

$\angle ADB = \angle BDC = 90^\circ$

(By the definition of a perpendicular bisector)

$AD=DC$ (By the definition of a perpendicular bisector)

Therefore, $\Delta ABD \cong \Delta BDC$ by Angle Side Angle(ASA) Postulate.

Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent.(CPCTC)

Answer 2

Blank 1: *ASA Postulate*
Blank 2: *CPCTC*

Based on the info. your given and I drew (screenshot). Blank 1 is ASA Post. and Blank 2 is CPCTC because of ASA Post.

i am so sorry!
I meant to draw line segment AD is congruent to AC.... However Line segment AB is congruent to BC....