Question

Write proofs in two-column form.

Given: $\overline{\mathbf{JM}}\cong \overline{\mathbf{LM}}$; $\overline{\mathbf{JK}}\cong \overline{\mathbf{LK}}$.

Prove: $\angle \mathbf{MJK}\cong \angle \mathbf{MLK}$

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$\overline{JM}\cong \overline{LM}$ and $\overline{JK}\cong \overline{LK}$.

In the triangles $▵MJK$and $▵MLK$, the side that is common is \[MK\].

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

In the triangles $▵MJK$and $▵MLK$, it can be noticed that $\overline{JM}\cong \overline{LM}$, $\overline{MK}\cong \overline{MK}$ and$\overline{JK}\cong \overline{LK}$.

Therefore, the triangles $▵MJK$ and $▵MLK$ are the congruent triangles by using the SSS postulate.

The triangles $▵MJK$ and $▵MLK$ are the congruent triangles.

Therefore, by using the corresponding parts of congruent triangles it can be said that $\angle MJK\cong \angle MLK$.

- Write the conclusion.

The proof in two-column form is: