Question

below is a typical geometric two-column proof that you will be able to complete by the end of your geometry course. but right now you only have a few postulates and theorems in your geometry toolbox. using what you already know about the vertical angles theorem, fill in step 3 of this proof.

Answer 1

Angles can be congruent based on various theorems.

In this case, the statement that completes the proof is: $\mathbf{\angle AMB \cong \angle DMC}$

The angles between two transverse lines are congruent.

The above statement means that, the vertical angles at the point of intersection of the transverse lines are congruent

This is so, because the two angles are vertical angles

From the diagram (see attachment), the vertical angles are:

• $\mathbf{\angle AMB}$
• $\mathbf{\angle DMC}$.

Because both angles are vertical angles, then:

$\mathbf{\angle AMB \cong \angle DMC}$

Read more about vertical angles at:

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