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Answer:
Question 1:
The angles are presented here using Autocad desktop application
The two column proof is given as follows;
Statement Reason
S1. Line m is parallel to line n R1. Given
S2. ∠1 ≅ ∠2 R2. Vertically opposite angles
S3. m∠1 ≅ m∠2 R3. Definition of congruency
S4. ∠2 and ∠3 form a linear pear R4. Definition of a linear pair
S5. ∠2 is supplementary to ∠3 R5. Linear pair angles are supplementary
S6. m∠2 + m∠3 = 180° Definition of supplementary angles
S7. m∠1 + m∠3 = 180° Substitution Property of Equality
S8. ∠1 is supplementary to ∠3 Definition of supplementary angles
Question 2:
(a) The property of a square that is also a property of a rectangle is that all the interior angles of both a square and a rectangle equal
(b) The property of a square that is not necessarily a property of all rectangles is that the sides of a square are all equal, while only the length of the opposite sides of a rectangle are equal
(c) The property of a rhombi that is also a property of a square is that all the sides of a rhombi are equal
(d) A property of a rhombi that is not necessarily a property of all parallelogram is that the diagonals of a rhombi are perpendicular
(e) A property that applies to all parallelogram is that the opposite sides of all parallelogram are equal
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