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`.