Question

determine whether the conclusion is valid based on the given information. select valid or invalid. explain your reasoning. given: right angles are congruent. ∠1 and ∠2 are right angles. conclusion: ∠1 ≅ ∠2 select choice v; select choice

Explanation:

Step1: Recall congruent right angles

A right angle measures \( 90^\circ \). By definition, if two angles are right angles, their measures are equal.

Step2: Apply congruence definition

Congruent angles have equal measures. Since \( \angle 1 \) and \( \angle 2 \) are right angles (each \( 90^\circ \)), their measures are equal. Thus, \( \angle 1 \cong \angle 2 \) by the definition of congruent angles (angles with equal measure are congruent).

Answer:

The conclusion \( \angle 1 \cong \angle 2 \) is valid because all right angles have a measure of \( 90^\circ \), so angles with equal measure (right angles here) are congruent.