Terrence's conjecture is that if two angles are supplementary, they must form a linear pair. A linear pair of angles is defined as two adjacent angles whose non-common sides form a straight line, summing up to 180°.

Supplementary angles, however, are simply two angles that add up to 180°, but they do not necessarily need to be adjacent or form a straight line.

Let's examine each figure:

• Figure A shows a triangle with an interior angle. There's no clear indication of two angles being supplementary.
• Figure B consists of two separate right triangles. These angles do not seem to offer any supplementary pair.
• Figure C is a single right triangle. Again, there's no clear supplementary pair.
• Figure D shows two separate angles of 125° each. These angles are not adjacent, but they are supplementary since their sum equals 180°.

Thus, Figure D is a counterexample to Terrence’s conjecture. The two angles are supplementary but do not form a linear pair, proving that his conjecture is incorrect.

Would you like more details or have any further questions?

Related Questions:

1. What is the difference between a linear pair and supplementary angles?
2. Can two right angles form a linear pair?
3. How can non-adjacent angles still be supplementary?
4. What are other examples of supplementary angles that are not a linear pair?
5. How does a counterexample disprove a mathematical conjecture?

Tip:

In geometry, a counterexample is a powerful way to disprove a statement. One example that violates the conditions is enough to show the conjecture is false.