Question

fill in the missing reasons for the proof of the theorem that all right angles are congruent. given: ∠f and ∠g are right angles. prove: ∠f≅∠g statements: 1) ∠f and ∠g are right angles. 2) m∠f = 90 and m∠g = 90 3) m∠f = m∠g 4) ∠f≅∠g reasons: 1) given 2) definition of right angles 3) substitution property of equality 4)

Explanation:

Step1: State the given information

Given that $\angle F$ and $\angle G$ are right - angles.

Step2: Use the definition of right - angles

By the definition of right - angles, if $\angle F$ is a right - angle then $m\angle F = 90$, and if $\angle G$ is a right - angle then $m\angle G=90$.

Step3: Apply the substitution property of equality

Since $m\angle F = 90$ and $m\angle G = 90$, we can substitute to get $m\angle F=m\angle G$.

Step4: Recall the definition of congruent angles

If $m\angle F=m\angle G$, then $\angle F\cong\angle G$ (by the definition of congruent angles: two angles are congruent if and only if their measures are equal).

Answer:

1. Given
2. Definition of right angles
3. Substitution Property of Equality
4. Definition of congruent angles