Name:______Per:______Date:______

Geometry

Chapter 6 Test A

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____1.Which statement is true?

a. / All quadrilaterals are rectangles.
b. / All quadrilaterals are squares.
c. / All rectangles are quadrilaterals.
d. / All quadrilaterals are parallelograms.

____2.For the parallelogram, if and find The diagram is not to scale.

a. / 9 / b. / 17 / c. / 173 / d. / 163

____3.Find values of x and y for which ABCD must be a parallelogram. The diagram is not to

scale.

a. / x = 10, y = 38 / b. / x = 10, y = 21 / c. / x = 10, y = 7 / d. / x = 7, y = 10

____4.If and find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale.

a. / x = 4,y = / c. / x = 11,y =
b. / x = 4,y = / d. / x = 11,y =

____5.DEFG is a rectangle. DF = 5x – 5and EG = x + 11. Find the value of x and the length of each diagonal.

a. / x = 4, DF = 13, EG = 13 / c. / x = 4, DF = 15, EG = 15
b. / x = 4, DF = 15, EG = 18 / d. / x = 2, DF = 13, EG = 13

____6.Find the values of aand b. The diagram is not to scale.

a. / / c. /
b. / / d. /

____7.The isosceles trapezoid is part of an isosceles triangle with a 46° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale.

a. / 67°; 134° / b. / 67°; 113° / c. / 46°; 134° / d. / 46°; 113°

____8.Which description does NOTguarantee that a trapezoid is isosceles?

a. / congruent bases
b. / congruent diagonals
c. / both pairs of base angles congruent
d. / congruent legs

____9.are base angles of isosceles trapezoid JKLM.If and (Draw a picture)

a. / 151 / b. / 1 / c. / 29 / d. / 75.5

____10.In quadrilateral MNOP, Which of a parallelogram, trapezoid, or rhombus could quadrilateral MNOP be? (Draw a picture)

a. / parallelogram or rhombus / c. / trapezoid only
b. / parallelogram only / d. / any of the three

Short Answer

11.Isosceles trapezoid ABCD has legs and and base If AB=4y–3, BC =3y–4, and CD=5y – 10, find the value of y. (Draw a picture)

12.Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale.

13.Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.

14.Complete this statement: For parallelogram ABCD,

Then state a definition or theorem that justifies your answer.

15.Find the values of the variables and the lengths of the sides of this kite.

16.ABCD is a parallelogram. If then The diagram is not to scale.

17.Find the values of the variables in the parallelogram. The diagram is not to scale.

18.Find in the kite. The diagram is not to scale.

19. and Find The diagram is not to scale.

20.ABCD is a parallelogram. If then The diagram is not to scale.

21.Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.

  1. Find the coordinates of the midpoint of the segment with the given endpoints.P( 10, -1) and Q( 7, 3)

23.In the rhombus, Find the value of each variable. The diagram is not to scale.

  1. One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 74 cm. Find the lengths of the sides of the kite.

25.Find the length of the segment. Simplify the radical!

EXTRA CREDIT

  1. Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S.(1 point)

R( -3, 7), M( 2, -4)

27.Write a proof (3 points)

Given:

Prove:VX = XT, SX = XU