Question

2 given: ∠1≅∠4 prove: ∠2≅∠3 statements reasons 1. ∠1≅∠4 1. given 2. m∠1 = m∠4 2. 3. m∠1 = m∠2; m∠3 = m∠4 3. def of congruence 4. m∠2 = m∠3 4. substitution 5. ∠2≅∠3 5. congruence prop

Explanation:

Step1: Define congruent angles

If two angles are congruent, their measures are equal. So if $\angle1\cong\angle4$, then $m\angle1 = m\angle4$.

Step2: Identify vertical - angle relationships

Vertical angles are congruent. $\angle1$ and $\angle2$ are vertical angles, so $m\angle1 = m\angle2$. Also, $\angle3$ and $\angle4$ are vertical angles, so $m\angle3 = m\angle4$.

Step3: Use substitution

Since $m\angle1 = m\angle4$, $m\angle1 = m\angle2$ and $m\angle3 = m\angle4$, we can substitute to get $m\angle2 = m\angle3$.

Step4: Define congruent angles again

If the measures of two angles are equal, the angles are congruent. So if $m\angle2 = m\angle3$, then $\angle2\cong\angle3$.

Answer:

1. Definition of congruent angles
2. Vertical angles are congruent
3. Definition of congruent angles