Question

I need help with #9. I am stuck on this problem.

Answer 1

Explanation:

Numbering the boxes top-to-bottom, left-to-right, you can develop the proof as follows:

1. ∠E ≅ ∠U . . . . given

2. SE ≅ SU . . . . given

3. ∠1 ≅ ∠2 . . . . vertical angles are congruent

Look at the diagram and locate these parts of the figure. You see that you have an angle at either end of line segment SE that is congruent to a corresponding angle at either end of line segment SU. That is, you have an Angle, a Segment, and an Angle (ASA) that correspond and are congruent.

You know that the angles at S correspond, the angles at E and U correspond, so the third vertex of those two triangles (M and O) will correspond. You need to be careful to write the corresponding vertices in the same order:

4. ΔMES ≅ ΔOUS . . . . by the ASA congruence theorem

5. MS ≅ SO . . . . CPCTC (corresponding parts of congruent triangles are congruent).

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Comment on the proof

Strictly speaking another step or two is required to show the above conclusion. The corresponding parts are MS and OS. Those are congruent by CPCTC. The next steps are to show OS ≅ SO by the symmetric property of congruence, then show MS ≅ SO by the transitive property of congruence because both are congruent to OS.