Proving That a Quadrilateral Is a Parallelogram: 1. equilateral 2. 128.6 3. 21 4. 720 degrees 5. x = 99 degrees 6. 96 degrees 7. 5 sides

Step-by-step explanation: 8. find the values of the variables x, y, and z in the parallelogram [109 + 33 + y = 180] [142 + y = 180] [y = 180 - 142] [y = 38] [z = 109 because opposite angles are congruent.] [x = 33 because both are alternate angles from each other.]

9. find the values of x and y.

DH = HF x + 1 = 3y, y = (x + 1)/3

GH = HE 3x - 4 = 5y + 1, y = (3x - 5)/5

solve for x --> (x + 1)/3 = (3x - 5)/5

5x = 9x - 20

5x - 9 = -9x - 20

4x = 20

4x/4 = 20/4

x = 5

solve for y

y = (x + 1)/3

y = (5 + 1)/3

y = 6 / 3

y = 2

10. OL = NM 3y - 6 = x - 5, 3y = x - 6 + 5, 3y = x - 1, y = 1/3x - 1/3

ON = LM 8x - 8 = 7x + 4, 8x + 8 + 7x + 4 + 8, 8x = 7x + 12, x = 12

y = 1/3(12) - 1/3

y = 4 - 1/3

y = 11/3

11. reasons 3. definition of parallelogram 4. alternate interior angles 5. reflexive property 6. ASA

12. Yes, both pairs of opposite angles are congruent.

13. Statements: 2. SV is II to TU 3. SVU equals UTS and VUT equals TSV Reasons: 7. Transversal parallel lines 8. Two pairs of angles are congruent