Complete the two-column proof by providing a reason for each of the five statements. Given: Rectangle R U T S Prove: ∠ U S R = ∠ S U T Statement Reason
1. R U T S is a rectangle
2. R U = S T ; U T = R S
3. ∠ S T U and ∠ S R U are right angles
4. △ U R S ≅ △ S T U
5. ∠ U S R = ∠ S U T

The two column proof can be presented as follows;

Statement                                              Reason

1. RUST is a rectangle                            Given

2. RU = ST ; UT = RS                              Definition of a rectangle

3. ∠STU and ∠SRU are right angles      Definition of a rectangle

4. ΔURS ≅ ΔSTU                                     By SAS rule of congruency

5. ∠USR = ∠SUT                                     By CPCTC            

Step-by-step explanation:

Given that the side RU, the angle ∠SRU and the side RS of triangle ΔURS are congruent to the side ST the angle ∠STU and the side UT of triangle ΔSTU, then ΔURS is congruent to ΔSTU, by the Side-Angle-Side (SAS) rule of congruency

Therefore, we have that ∠USR ≅ ∠SUT and therefore, it can be shown that ∠USR = ∠SUT using the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.

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step-by-step explanation: