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? ∠abc, ∠def are right angles → m∠abc = 90°, m∠def = 90° → m∠abc = m∠def → ∠abc≅∠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 degrees. So, since $\angle ABC$ and $\angle DEF$ are right - angles, $m\angle ABC = 90^{\circ}$ and $m\angle DEF=90^{\circ}$.

Step2: Transitive property of equality

If $a = c$ and $b = c$, then $a = b$. Here, $m\angle ABC = 90^{\circ}$ and $m\angle DEF = 90^{\circ}$, so $m\angle ABC=m\angle DEF$ by the transitive property of equality.

Step3: Definition of congruent angles

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

Answer:

A. Definition of right - angle
B. Transitive property of equality
C. Definition of congruent angles