Question 1

Which of the following conditions is NOT sufficient to prove that a quadrilateral is a parallelogram?

Accepted Answer

Two angles are supplementary.

Answer

Two diagonals bisect each other.

Answer

Two pairs of sides are parallel.

Answer

Two pairs of opposite sides are congruent.

Question 2

In the diagram below, parallelogram ABCD has diagonals $\overline{AC}$ and $\overline{BD}$ that intersect at point E. Which expression is not always true?

Accepted Answer

$\overline{AC}$

Answer

$\overline{AC}\cong\ \overline{BD}$

Answer

$\overline{AC}\cong\ \overline{BD}$

Answer

$\overline{AC}\cong\ \overline{BD}$

Question 3

In quadrilateral RSTW, diagonals $\overline{AC}$ are perpendicular bisectors of each other. Quadrilateral RSTW must be a:

I. Rectangle

II. Rhombus

III. Square

Accepted Answer

II and III

Answer

I

Answer

I, II, III

Answer

I, II

Question 4

What condition will make parallelogram WXYZ a rectangle?

Accepted Answer

$\overline{AC}\cong\ \overline{BD}$ is a right angle

Answer

$\overline{AC}\cong\ \overline{BD}$

Answer

$\overline{AC}\cong\ \overline{BD}$

Answer

$\overline{AC}\cong\ \overline{BD}$

Question 5

LMNO is a parallelogram. If NM = x + 15 and OL= 3x + 5, find the value of x and then find NM and OL.

Accepted Answer

x =5; NM = 20; OL = 20

Answer

x = 7; NM = 20; OL = 22

Answer

x = 7; NM = 22; OL = 22

Answer

x= 5; NM = 22; OL = 20

Question 6

Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.

Accepted Answer

Yes, opposite angles are congruent.

Answer

No, you cannot prove that the quadrilateral is a parallelogram.

Answer

Yes, opposite sides are congruent.

Answer

Yes, two opposite sides are both parallel and congruent.

Question 7

Based on the information in the diagram, can you prove that the quadrilateral must be a parallelogram? Explain.

Given:XY WZ and XW YZ

Accepted Answer

Yes, opposite sides are congruent.

Answer

No, you cannot determine that the quadrilateral isa parallelogram.

Answer

Yes, two opposite sides are both parallel andcongruent.

Answer

Yes, diagonals of a parallelogram bisect each other.

Question 8

In parallelogram FGHI, diagonals IG and FH are drawn to intersect at point M. Which of the following statements must be TRUE?

Accepted Answer

$\overline{AC}\cong\ \overline{BD}$ GMH must be congruent to IMF.

Answer

$\overline{AC}\cong\ \overline{BD}$ HGI must be an acute triangle.

Answer

$\overline{AC}\cong\ \overline{BD}$ FMG must be congruent to HMG.

Answer

$\overline{AC}\cong\ \overline{BD}$ FGHI must be an obtuse triangle.

Question 9

Given that ABCD is a parallelogram. A student wrote the proof below to show that a pair of its opposite angles are congruent. What is the reason justifying that ∠B ≅ ∠D?

Accepted Answer

Corresponding parts of congruent triangles are congruent.

Answer

Parallel lines have congruent corresponding angles.

Answer

Alternate interior angles in congruent triangles are congruent.

Answer

Oppositeangles in a quadrilateral are congruent.

Question 10

Parallelogram ABCD is shown. Which pair of triangles can be established to be congruent to prove that $\overline{AC}$ DAB $\overline{BD}$ $\angle$ BCD?

Accepted Answer

$\overline{AC}\cong\ \overline{BD}$ DAB and $\Delta$ BCD

Answer

$\overline{AC}\cong\ \overline{BD}$ ADC and $\Delta$ BCD

Answer

$\overline{AC}\cong\ \overline{BD}$ AED and $\Delta$ BEC

Answer

$\overline{AC}\cong\ \overline{BD}$ DEC and $\Delta$ BEA

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