(a). Draw trapezoid ABCD. Let E and F be points on $\overleftrightarrow{A B}$ such that $\overrightarrow{C E} \perp \overleftrightarrow{A B}$ and $\overrightarrow{D F} \perp \overleftrightarrow{A B}$.

(b). Prove that CE=DF.

($c$). Let AB=$b_1, CD=b_2$, and CE=DF=h. Prove that the area of trapezoid ABCD is $\frac{h}{2}\left(b_1+b_2\right)$.

The diagonals of square ABCD intersect at M. If m∠AMD = x + 2y and m∠ABC = 2x - y, find the values of x and y.

The diagonals of rectangle ABCD intersect at E. AE = y + 12 and DE= 3y - 8. Find AE, DE, AC, and BD.

The diagonals of rhombus ABCD intersect at E. Name a pair of perpendicular line segments.

The coordinates of the image of A(3, -2) under a reflection in the x-axis are (1) (3, 2) (2) (-3, 2) (3) (-3, -2) (4) (-2, 3)

Quadrilateral ABCD is a parallelogram, M is a point on $\overline{A B}$, and N is a point on $\overline{C D}$. If $\overline{C M} \| \overline{A N}$, prove that $\triangle A N D \cong \triangle C M B$.

ABCD is an isosceles trapezoid, A̅B̅ || D̅C̅, and AD ≅ BC. lf AD = 2y - 5 and BC = y + 3, find AD.

The diagonals of square ABCD intersect at M. If AB = a+ b, BC = 2a, and CD = 3b - 5, find AB, BC, CD, and DA.

Find the area of a triangle whose vertices are (-1, -1), (7, -1), and (3, 5).

ABCD is a parallelogram. The degree measure of ∠A is represented by 2x + 10 and the degree measure of ∠B by 3x. Find the value of x, of m∠A, and of m∠B.

What is the slope of a line that is parallel to the line whose equation is 3x + y = 5? (1)-3 (2)-5/3 (3)5/3 (4)3

The diagonals of square ABCD intersect at M. If AC = 3x + 2 and BD = 7x - 10, find AC, BD, AM, BM.

Quadrilateral ABCD is a parallelogram, M is a point on $\overline{A B}$, and N is a point on $\overline{C D}$. If $\overline{D M} \perp \overline{A B}$ and $\overline{B N} \perp \overline{C D}$, prove that $\triangle A M D \cong \triangle C N B$.

ABCD is an isosceles trapezoid, A̅B̅ || D̅C̅, and AD ≅ BC. If AD = 3x + 7 and BC = 25, find the value of x.