Question

1. given: abc, db⊥ac, and m∠1 = m∠2. prove: m∠3 = m∠4. statements reasons

Explanation:

Step1: State the given information

Given: $\overline{DB}\perp\overline{AC}$, $m\angle1 = m\angle2$

Step2: Recall the property of perpendicular lines

Since $\overline{DB}\perp\overline{AC}$, $\angle ABD$ and $\angle CBD$ are right - angles. So, $m\angle ABD=m\angle CBD = 90^{\circ}$.

Step3: Express $\angle ABD$ and $\angle CBD$ in terms of smaller angles

$\angle ABD=\angle3+\angle1$ and $\angle CBD=\angle4+\angle2$.

Step4: Substitute the equalities

Because $m\angle ABD = m\angle CBD$ and $m\angle1 = m\angle2$, we have $\angle3+\angle1=\angle4+\angle2$.

Step5: Use the subtraction property of equality

Subtract $\angle1$ (which is equal to $\angle2$) from both sides of the equation $\angle3+\angle1=\angle4+\angle2$. We get $m\angle3=m\angle4$.

Answer:

The proof that $m\angle3 = m\angle4$ is completed as shown above.