state which lines, segments, or rays are parallel in these figures and state the postulate or theorem which proves them parallel. 1.          this is an uneven...

state which lines, segments, or rays are parallel in these figures and state the postulate or theorem which proves them parallel.

1.          this is an uneven rectangle               D_________________________C

                                                                 A_______________________B

      corner of D is 95 degrees, corner of C is 80 degrees, corner of A is 85 degrees and corner  of B is 100 degrees

2.      this is a rectangle                               H__________________________G

                                                                          34 degrees

                                                                                                        58 degrees

                                                                   90 degrees          34 deg.

                                                                 E___________________________F

A line is drawn from H to F.  At corner F the bottom left corner is 34 degrees, and the bottom right of corner F is 58 degrees.

At corner H, the top right corner is 34 degrees.  Corner E is 90 degrees.  Letter G is not labled with degrees.

3.  

                                                                 O

                              P

                             42

                                               28

                         L_________________________M_____

                                                       N

                              38

                                             32

                    J____________________________K_____

A continuous lines connects P, L and J.  A line connects L to O.  A line connects J to N

Thank you :)

Expert Answers
gsenviro eNotes educator| Certified Educator

1. AB is parallel to CD 

using consecutive interior angle theorem (converse), since the sum of <ABC and <BCD is 180 (100 + 80), the lines are parallel. We can check the same with <BAD + <ADC =180 also.

2. EF and GH are parallel to each other.

Using alternate interior angle theorem (converse), bottom left at F and top right angle at H are equal (to 34 degrees), proves that EF and GH are parallel.

3. LM and JK are parallel to each other

Using Corresponding angle postulate, the sum of corresponding angles <PLM (42+28 =70) is equal to <LJK (38+32 =70).