🧾 Proofs (Step by Step)

Question 1

What is the point of a proof?

Answer 1

A proof is like a math detective story. You start with the facts (givens), then logically prove the conclusion using definitions, theorems, and properties.

Question 2

How does a 2-column proof work?

Answer 2

Left column = statements (what you claim is true).
Right column = reasons (why it’s true).
Each statement must match a reason → like evidence in court.

Question 3

Example Proof: Base angles of an isosceles triangle are equal.

Answer 3

Start: AB = AC (Given)

Draw the angle bisector from A to side BC (Construction)

Now you have 2 smaller triangles.

They share side AD (Reflexive property).

AB = AC (Given), AD = AD (Reflexive), and ∠BAD = ∠CAD (Construction).

Triangles are congruent (SAS).

Therefore, ∠B = ∠C (CPCTC = corresponding parts of congruent triangles are congruent).