# 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 :)

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### 1 Answer

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).