Question

using flowchart proofs
given: \\( \angle abc \\) is a right angle and \\( \angle def \\) is a right angle.
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: Definition of right angle

By the definition of a right - angle, if an angle is a right - angle, its measure is \(90^{\circ}\). Since \(\angle ABC\) and \(\angle DEF\) are right - angles (given), we have \(m\angle ABC = 90^{\circ}\) and \(m\angle DEF=90^{\circ}\).

Step2: Substitution property of equality

We know that \(m\angle ABC = 90^{\circ}\) and \(m\angle DEF = 90^{\circ}\). By the substitution property of equality (if \(a = c\) and \(b = c\), then \(a = b\)), substituting \(c = 90^{\circ}\), \(a=m\angle ABC\), and \(b = m\angle DEF\), we get \(m\angle ABC=m\angle DEF\).

Step3: Definition of congruent angles

Two angles are congruent if and only if their measures are equal. Since \(m\angle ABC=m\angle DEF\), by the definition of congruent angles, \(\angle ABC\cong\angle DEF\).

Answer:

A: Definition of right angle; B: Substitution property of equality; C: Definition of congruent angles.