Question

prove: all right angles are congruent by showing that \\( \angle abc \cong \angle def \\).
what are the missing reasons in the steps of the proof?
\\( \angle abc, \angle def \\) are right angles \\( m \angle abc = 90 ^ { \circ }, m \angle def = 90 ^ { \circ } \\) \\( m \angle abc = m \angle def \\) \\( \angle abc \cong \angle def \\)
given a b c
a:

b:

c:

Explanation:

Step1: Determine Reason for A

A right angle is defined as an angle with a measure of \( 90^\circ \). Since \( \angle ABC \) and \( \angle DEF \) are given as right angles, by the definition of a right angle, their measures are \( 90^\circ \). So the reason for A is "Definition of a right angle".

Step2: Determine Reason for B

We know \( m\angle ABC = 90^\circ \) and \( m\angle DEF = 90^\circ \). By the transitive property of equality (or simply recognizing that two quantities equal to the same quantity are equal to each other), we can conclude \( m\angle ABC = m\angle DEF \). So the reason for B is "Transitive property of equality (or substitution, since both equal \( 90^\circ \))".

Step3: Determine Reason for C

If two angles have equal measures, then the angles are congruent. This is the definition of congruent angles (angles with equal measures are congruent). So the reason for C is "Definition of congruent angles".

Answer:

A: Definition of a right angle
B: Transitive property of equality (or Substitution)
C: Definition of congruent angles