Which would be the next step to prove that the base angles of the increment A B C are congruent in the FEWEST steps possible?

Answer 1

Given: Triangle ABC is isosceles with AB ≅ AC.

Proof: ∠ABC ≅ ∠ACB.

Step 1. Draw the perpendicular bisector from vertex A to base BC, and let's call the point where it intersects BC as point D.

Step 2. In triangles ABD and ACD, show that:

AB ≅ AC (Given)

AD ≅ AD , due to the reflexive property of congruence

BD ≅ CD , since AD bisects BC

Step 3. By the Side-Side-Side Postulate, conclude that ΔABD ≅ ΔACD.

Step 4. By Corresponding Parts of Congruent Triangles are Congruent, ∠ABC ≅ ∠ACB.

This approach only involves 4 steps and uses the properties of isosceles triangles along with basic congruence postulates.