Question

Complete the two-column proof by providing a reason for each of the five statements.

Answer 1

Answer:

The given two column proof can be completed as follows;

Statement     ${}$                               Reason

1. RUTS is a rectangle      ${}$                          1. Given

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

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

4. ΔURS ≅ ΔSTU               ${}$                         4. By SAS rule of congruency

5. ∠USR = ∠SUT      ${}$                                   5. By CPCTC

Step-by-step explanation:

The Side-Angle-Side (SAS) rule of congruency states that where we have two sides and an included angle of one triangle, congruent to the corresponding two sides and included angle of another triangle, the two triangles are congruent

The Congruent Parts of Congruent Triangles are Congruent (CPCTC) postulate is made use of the serve as proof that two parts of a triangle are congruent when it has been proven that the two triangles are congruent.

Answer 2

Answer:

Proof is stated below.

Step-by-step explanation:

Given: RUTS is a rectangle.

To Prove: <USR = <SUT

Therefore,

Given: RUTS is a rectangle.

RU = ST ; UT = RS - Definition of a parallelogram / rectangle; sides are of equal measure.

<STU & <SRU are right angles ; Definition of a rectangle; a rectangle has four right angles.

Triangle URS is congruent to triangle STU; SAS theorem.

<USR = <SUT; CPCTE.

Hence, proved.