Question

In ∆ABC shown below, ∡BAC is congruent to ∡BCA. Given: Base ∡BAC and ∡ACB are congruent.
Prove: ∆ABC is an isosceles triangle.

Answer 1

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 _______1________.
∆BAD is congruent to ∆BCD by the _______2________. Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

Answer 2

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

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

c) 1. the definition of a perpendicular bisector
2. Angle-Side-Angle (ASA) Postulate

d) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector

Answer 3

@AkashdeepDeb

Answer 4

Just hold on..

Answer 5

ok

Answer 6

See I don't really think we can draw a perpendicular bisector from B!
Yes from our knowledge we know that in an isosceles traingle there can be a perpendicular bisector but we have to PPROVE that!
So we can only drop a Perpendicular and not a perpendicular bisector! :)