Question

Geometry one last ? thanks

Answer 1

Given:

$SP\cong MO,\angle P\cong \angle O$

To find:

The additional pair of corresponding parts that needs to be congruent in order to prove that $\Delta STP\cong \Delta MKO$ by ASA.

Solution:

According to ASA, two triangles are congruent if their two corresponding angles are congruent and their included sides of those angles are also congruent.

In $\Delta STP\text{ and }\Delta MKO$,

$\angle P\cong \angle O$                            [Given]

$SP\cong MO$                                      [Given]

Clearly, SP is between angle S and angle P, and MO is between angle M and angle O.

Then, $\angle S\cong \angle M$ as $\Delta STP\cong \Delta MKO$ by ASA.

Therefore, the additional pair of corresponding parts that needs to be congruent in order to prove that $\Delta STP\cong \Delta MKO$ by ASA is $\angle S\cong \angle M$.