Exploring Quadrilaterals

Two Quadrilaterals are described. Quadrilateral H - has four right angles Quadrilateral R - has two pairs of parallel sides. Which statement MUST be true based on the given information?

• The diagonals of Quadrilateral R are congruent.

• The diagonals of Quadrilateral H are congruent.

• The diagonals of Quadrilateral H are not congruent

• The diagonals of Quadrilateral R are not congruent.

Two quadrilaterals are described. Quadrilateral M - has four equal sides. Quadrilateral N - has exactly one pair of parallel sides and congruent diagonals. Select all statements that MUST be true based on the given information.

• Opposite angles of Quadrilateral M are congruent.

• Opposite angles of Quadrilateral N are congruent.

• Consecutive angles of Quadrilateral M are supplementary.

• Base angles of Quadrilateral N are congruent.

• The nonparallel sides of Quadrilateral N are congruent.

Trapezoid RCZM is shown where L is the midpoint of RM, F is the midpoint of CZ.

RC= 3x, LF= 5x-2, MZ= 4x+2, Determine the value of x.

• x= 1

• x= 2

• x = 3

• x = 4

The regulations for a paper airplane making contest state that all paper airplanes must be in the shape of an isosceles trapezoid. Andrew used computer software to sketch a trapezoid, as shown. Some measurements, in centimeters, are shown. MH = 15.2 cm., FL = 10 cm., FM = 13 cm., NL = 15 cm., MG = 4 cm. How long is diagonal FH? Round your answer to the nearest whole number.

• FH = 20 cm

• FH = 25 cm

• FH = 400 cm

• FH = 169 cm

Select the correct shapes that can all be classified as a polygon, quadrilateral, and special parallelograms.

• A. Square

• B. Kite

• C. Rhombus

• D. Rectangle

• E. Trapezoid

ABCD is a parallelogram whose diagonals intersect at point E. Some measurements are given. AB = 8x + 5.5, AD = 4x + 2.5, AE = 3x+8.5, AC = 50. What is the value of x?

• x = 10.5

• x = 5.5

• x = 25

• x = 33

What is Reason 2?

• Opposite angles of a parallelogram are supplementary.

• Opposite angles of a parallelogram are congruent.

• Opposite sides of a parallelogram are congruent.

• Opposite sides of a parallelogram are not congruent.

What is Reason 3?

• Opposite angles of a parallelogram are supplementary.

• Opposite angles of a parallelogram are congruent.

• Opposite sides of a parallelogram are congruent.

• Opposite sides of a parallelogram are not congruent.

What is Reason 4?

• Opposite angles of a parallelogram are supplementary.

• Opposite angles of a parallelogram are congruent.

• Opposite sides of a parallelogram are congruent.

• Given

Trapezoid RCZM is shown where L is the midpoint of RM, F is the midpoint of CZ.

RC= 3x, LF= 5x-2, MZ= 4x+2, What is the length of LM if RM = 8x+5?

• LM = 21.5

• LM = 2.5

• LM = 4.5

• LM = 10.5