Prove the conjecture true or false and give a counterexample if false

Question

Given: Segment FG is congruent to Segment GH

Conjecture: G is the Midpoint of Segment FH

 

2. Given: Angle A and Angle B are supplementary

    Conjecture: Angle A and Angle B are adjacent angles.

Answer 1

For G to be midpoint of FH, F, G, and H must be collinear. That is not stated in the conjecture.

 

Adjacent angles share a vertex and a side. Two angles can be supplementary and not be adjacent, e.g., consecutive angles of a parallelogram.