Question

Geometry: complete this proof of theorem 18, ASAP!!!

(Theorem 18: if the side of one angle are parallel to the sides of another angle, right side to left side and left side to right side, then the angle are supplementary)

Answer 1

Supplementary angles are angles that can be summed up to give $180^{o}$, which is the value of the sum of angles on a line.

The required statements and reasons are given below:

Two or more lines are said to be parallel if there is no measure of the angle between them or the measure of the angle between them is $180^{o}$. Thus the lines would never meet at any point even when extended to infinity.

While supplementary angles are angles that can be summed up to give $180^{o}$, which is the value of the sum of angles on a line.

               STATEMENTS                                        REASONS

1. < A and <B with AD ║BE, AC ║BF                   Given.

2. AD, AC, BE, BF                                                 Straight line.

3. <A ≅ <1                                                              Congruent property of

                                                                              vertically opposite angles.

4. AD + AC  ≅ DC                                                 Addition property of parts

   BE + BF  ≅ EF                                                   of a given line segment.                                    

5. <A + <B ≅ $180^{o}$                                                 Addition property of

                                                                            supplementary angles.  

For more clarifications on the properties of parallel lines, visit: https://brainly.com/question/24607467

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