Question

in the figure, line ab intersects line cd to form four angles. the table shows an incomplete proof that ∠1≅∠2. drag the correct step and reason to complete the proof.

1. m∠1 + m∠3 = 180°; m∠2 + m∠3 = 180° (linear pair postulate)
2. (substitution property)
3. m∠1 = m∠2
4. ∠1≅∠2 (definition of congruence)

Explanation:

Step1: Identify linear - pair angles

By the linear - pair postulate, $\angle1$ and $\angle3$ are a linear pair, so $m\angle1 + m\angle3=180^{\circ}$, and $\angle2$ and $\angle3$ are a linear pair, so $m\angle2 + m\angle3 = 180^{\circ}$.

Step2: Use substitution property

Since $m\angle1 + m\angle3=180^{\circ}$ and $m\angle2 + m\angle3 = 180^{\circ}$, we can substitute the right - hand sides of the equations. So $m\angle1 + m\angle3=m\angle2 + m\angle3$.

Step3: Apply subtraction property

Subtract $m\angle3$ from both sides of the equation $m\angle1 + m\angle3=m\angle2 + m\angle3$. We get $m\angle1=m\angle2$.

Step4: Use definition of congruence

If $m\angle1=m\angle2$, then by the definition of congruence, $\angle1\cong\angle2$.

Answer:

The steps and reasons to complete the proof are as follows:

Steps	Reasons
2. $m\angle1 + m\angle3=m\angle2 + m\angle3$	Substitution property
3. $m\angle1=m\angle2$	Subtraction property
4. $\angle1\cong\angle2$	Definition of congruence