Questions: Quiz: Proving Angles Congruent CR Geometry A (GP) 24-25 / 2:Reasoning and Proof 1. angle 1 and angle 2 are supplementary and angle 1 is congruent to angle 2. Which one of these statements will always be angle 1 and angle 2 are right angles angle 1 and angle 2 are complementary angles angle 1 and angle 2 are adjacent angles angle 1 and angle 2 are vertical angles

The answer is the first one: $\angle 1$ and $\angle 2$ are right angles.

Explanation for each option:

1. $\angle 1$ and $\angle 2$ are right angles: This statement is correct. Since $\angle 1$ and $\angle 2$ are supplementary, their measures add up to 180 degrees. Given that $\angle 1 \cong \angle 2$, they are congruent, meaning they have the same measure. Therefore, each angle must be 90 degrees (since 90 + 90 = 180). Hence, $\angle 1$ and $\angle 2$ are right angles.

2. $\angle 1$ and $\angle 2$ are complementary angles: This statement is incorrect. Complementary angles add up to 90 degrees, but since $\angle 1$ and $\angle 2$ are supplementary, they add up to 180 degrees.

3. $\angle 1$ and $\angle 2$ are adjacent angles: This statement is incorrect. While $\angle 1$ and $\angle 2$ could be adjacent, it is not necessarily always true. Supplementary angles do not have to be adjacent; they just need to add up to 180 degrees.

4. $\angle 1$ and $\angle 2$ are vertical angles: This statement is incorrect. Vertical angles are formed by two intersecting lines and are always equal, but they are not necessarily supplementary. The given information only states that $\angle 1$ and $\angle 2$ are supplementary and congruent, not that they are vertical angles.

In summary, the correct statement is that $\angle 1$ and $\angle 2$ are right angles.