Question

Write proofs in two-column form.

Given: $\angle \mathbf{JMK}\cong \angle \mathbf{LMK}$; $\overline{\mathbf{MK}}$$\perp$plane $\mathbf{P}$.

Prove: $\overline{\mathbf{JK}}\cong \overline{\mathbf{LK}}$

Short answer

The proof in two-column form is:

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Description of step.

It is being given that$\angle JMK\cong \angle LMK$ and $\overline{MK}$$\perp$plane $P$.

In the triangles $▵MKJ$and $▵MKL$, the side that is common is $MK$.

Therefore, $\overline{MK}\cong \overline{MK}$by using the reflexive property.

As, $\overline{MK}$$\perp$plane $P$, therefore $m\angle MKJ=90°$ and $m\angle MKL=90°$.

Therefore, $\angle MKJ\cong \angle MKL$.

In the triangles $▵MKJ$and $▵MKL$, it can be noticed that $\angle JMK\cong \angle LMK$, $\overline{MK}\cong \overline{MK}$ and$\angle MKJ\cong \angle MKL$.

Therefore, the triangles $▵MKJ$ and $▵MKL$ are the congruent triangles by using the ASA postulate.

The triangles $▵MKJ$ and $▵MKL$ are the congruent triangles.

Therefore, by using the corresponding parts of congruent triangles it can be said that $\overline{JK}\cong \overline{LK}$.

- Write the conclusion.

The proof in two-column form is: