Question

given: ∠abc is a right angle and ∠def is a right angle. prove: all right angles are congruent by showing that ∠abc ≅ ∠def. what are the missing reasons in the steps of the proof? flowchart: ∠abc, ∠def are right angles (given) → m∠abc = 90°, m∠def = 90° (a) → m∠abc = m∠def (b) → ∠abc ≅ ∠def (c) dropdown options for a: definition of right angle; b: definition of congruent, definition of equal; c: definition of 90 degrees

Explanation:

• Step A: A right angle is defined as an angle with measure \( 90^\circ \), so the reason for \( m\angle ABC = 90^\circ, m\angle DEF = 90^\circ \) is the definition of right angle.
• Step B: Since both angles have measure \( 90^\circ \), \( m\angle ABC = m\angle DEF \) follows from the transitive property of equality (or recognizing equal measures from Step A), but the option "definition of equal" (interpreting equal angle measures) fits here as we equate the measures.
• Step C: Angles with equal measures are congruent by the definition of congruent angles (congruent angles have equal measures).

Answer:

• A: definition of right angle
• B: definition of equal
• C: definition of congruent