ANSWERS:
Determining whether the given quadrilateral is a parallelogram or not.
For Number One.
[tex] \large \tt Parallelogram[/tex]
• Opposite Sides are parallel.
• Opposite Sides are congruent.
For Number Two.
[tex] \large \tt Not \: \:Parallelogram[/tex]
• The given quadrilateral is a trapezoid. It has only one pair of parallel sides.
• The diagonals of a parallelogram bisect each other and separates it into two congruent triangles. In the case of trapezoid, the diagonal does not divide the quadrilateral into two equal triangles.
For Number Three.
[tex] \large \tt Parallelogram[/tex]
• Opposite Angles are congruent.
• Opposite Sides are congruent.
ANGLE MEASURES:
> Angle K isn't included in the illustration, so I'll just give the measure of the angles given.
[tex] \tt \angle L \cong \angle V[/tex]
[tex] \tt (9a + 12) \degree = (8a + 20) \degree[/tex]
[tex] \tt 9a + 12 = 8a + 20[/tex]
[tex] \tt 9a -8a = 20 - 12[/tex]
[tex] \tt a = 8[/tex]
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex] \begin{array}{l}\tt \angle L = 9a + 12 = 9(8) + 12 = 84 \degree\\ \tt \angle V =8a + 20 = 8(8) + 20 = 84 \degree \\ \tt \angle O = 180 \degree - \angle L = 180 \degree - 84 \degree = 96 \degree \\ \tt \angle E \cong \angle O; \: \angle E \ = 96 \degree \end{array}[/tex]
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
b. Find the measure of the line segment OV.
[tex] \tt\overline{LE}\cong \overline{OV}[/tex]
[tex] \tt (7x - 1)cm = (12x - 24)cm[/tex]
[tex] \tt 7x - 1 = 12x - 24[/tex]
[tex] \tt - 1 + 24 = 12x - 7x[/tex]
[tex] \tt 23 = 5x[/tex]
[tex] \tt \frac{23}{5} = \frac{5x}{5} \\ [/tex]
[tex] \tt x = 4.6[/tex]
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex] \begin{array}{l}\tt\overline{LE} = 7x - 1 = 7(4.6) - 1 = 31.2 \: cm\\ \tt \overline{OV} = 12x - 24 = 12(4.6) - 24 = \boxed{ \tt 31.2 \: cm}\end{array}[/tex]
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
