Review for Quadrilateral TEST

The diagonals of rectangle ABCD intersect at point E.

If AE = 2x + 5, and BD = 5x + 2, what is AC?

Katie would like to know if quadrilateral ABCD is a parallelogram. Determine which of the following methods would help her prove ABCD is a parallelogram.

• Find the distance of each side

• Find the slope of each side

• Find the angle measure of all four vertices

• Find the slope of the two diagonals

Parallelogram ABCD has diagonal segments AC and BD that intersect at E .

If BE is ( x + 8) and ED is (5 x ), find the length of BD.

A rectangle is a parallelogram. What is true of the diagonals of a rectangle that is not true of the diagonals of a parallelogram, in general?

• They are congruent

• They are perpendicular

• They bisect the angles of the rectangle

• They bisect each other

Consider a quadrilateral and its diagonals. Which conjecture below would best describe a quadrilateral whose diagonals divide it into four isosceles triangles?

• It is a square

• It is a rhombus

• It is an isosceles trapezoid

• It is a rectangle

Which of the following is sufficient alone to define a square?

I. A parallelogram with 4 congruent sides

II. A parallelogram with 4 right angles

III. A rectangle with 4 congruent sides

IV. A rhombus with 4 right angles

V. A parallelogram with congruent diagonals

• I and II only

• I, II, & IV only

• III and IV only

• III, IV, & V only

Concrete workers are busy preparing to pour a rectangular patio on the rear of David’s new house. The workers have laid out, using boards, what appears to be a rectangle to frame where the cement will go.

What could the workers do to ensure that the patio is really rectangular before pouring the cement?

• Determine if opposite sides are congruent.

• Determine if the diagonals are congruent.

• Determine if the diagonals are perpendicular.

Which of the following would NOT be true of a rhombus?

• 2 sets of parallel lines

• 4 acute angles

• Congruent opposite angles

• 4 equal sides

Which of the following quadrilaterals is best represented in the following description?

A plane figure with two sets of parallel sides, with one pair longer than the other, and at least one right angle.

• square

• rhombus

• rectangle

• parallelogram

Three vertices of a parallelogram are shown on a coordinate plane below.

Which coordinate pair could not be the fourth vertex of the parallelogram?

• (-4,-3)

• (6,-1)

• (-5,-3)

• (0,7)