Question

choose a method complete the flowchart proof. given $overline{jk}perpoverline{jm}$, $overline{kl}perpoverline{ml}$, $angle jcongangle m$, $angle kcong l$. prove $overline{jm}perpoverline{ml}$ and $overline{jk}perpoverline{kl}$

Explanation:

Step1: Analyze left - hand side of flowchart

Since $\overline{JK}\perp\overline{JM}$ (given), by the definition of perpendicular lines, $\angle J$ is a right - angle, so $m\angle J = 90^{\circ}$. Given $\angle J\cong\angle M$, by the definition of congruent angles, $m\angle J=m\angle M$. Then, by the substitution property of equality, $m\angle M = 90^{\circ}$. By the definition of a right - angle, $\angle M$ is a right - angle, and by the definition of perpendicular lines, $\overline{JM}\perp\overline{ML}$.

Step2: Analyze right - hand side of flowchart

Since $\overline{KL}\perp\overline{ML}$ (given), by the definition of perpendicular lines, $\angle L$ is a right - angle, so $m\angle L = 90^{\circ}$. Given $\angle K\cong\angle L$, by the definition of congruent angles, $m\angle K=m\angle L$. Then, by the substitution property of equality, $m\angle K = 90^{\circ}$. By the definition of a right - angle, $\angle K$ is a right - angle, and by the definition of perpendicular lines, $\overline{JK}\perp\overline{KL}$.

Answer:

Left - hand side (from top to bottom): $\angle J$ is a right angle; $m\angle M = 90^{\circ}$; $\angle M$ is a right angle
Right - hand side (from top to bottom): $m\angle L = 90^{\circ}$; $\angle K$ is a right angle; $m\angle K = 90^{\circ}$