Suppose each matchstick has length 1 inch. Using 12 such matchsticks, form a fig

Suppose each matchstick has length 1 inch. Using 12 such matchsticks, form a figure with area 4 square inches.

6a. In triangle ABC, draw through A a line perpendicular to BC. Choose any point M on this line. Prove: MB² − MC² = AB² − AC².

6b. In triangle ABC, suppose a point M in the plane satisfies MB² − MC² = AB² − AC². Prove that AM ⟂ BC.