Question

given mnpq is a parallelogram, with diagonals \\(\overline{mp}\\) and \\(\overline{nq}\\) that intersect at point e. if \\(ne = \frac{2}{3}x\\) and \\(eq = x - 10\\), what is the value of x?

select one:
a. 30
b. -6
c. 6
d. -30

which of the following is always true for a parallelogram?

select one:
a. all four sides are congruent.
b. opposite angles are congruent.
c. all angles are right angles.
d. all sides are perpendicular.

if \\(ki = 8x - 2\\), \\(dn = 7x + 7\\), \\(in = x - 4\\), and \\(kd = 2y + 3\\), find the values of x and y so that kind is a parallelogram.

Explanation:

Equate the diagonal segments of the parallelogram

$$
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$$

Solve the linear equation for x

$$
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$$

Evaluate the properties of a parallelogram

$$
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Set up equations for parallelogram KIND

$$
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$$

Solve for x and y

$$
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$$

Answer:

Question 1

• o a. 30 (Correct answer)
• o b. -6
• o c. 6
• o d. -30

Question 2

• o a. All four sides are congruent.
• o b. Opposite angles are congruent. (Correct answer)
• o c. All angles are right angles.
• o d. All sides are perpendicular.

Question 3

\(x = 9\), \(y = 1\)