Proving a Quadrilateral Is a Parallelogram Answers

1

Free Preview

What must the length of segment AD be for the quadrilateral to be a parallelogram?

A

8 units

B

16 units

C

31 units

D

62 units

1

Free Preview

What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply.

A

ML ∥ NO

B

ML ⊥ LO

C

LO ≅ MN

D

ML ≅ LO

E

MN ⊥ NO

1

Based on the measures shown, could the figure be a parallelogram?

A

Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.

B

Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.

C

No, there are three different values for x when each expression is set equal to 10.

D

No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

1

Based on the given information, which statement best explains whether the quadrilateral is a parallelogram?

A

It cannot be determined from the information given.

B

It is not a parallelogram because the congruent sides cannot be parallel.

C

It is not a parallelogram because the parallel sides cannot be congruent.

D

It is a parallelogram based on the single opposite side pair theorem.

1

Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.

A

∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.

B

WY ≅ WY by the reflexive property.

C

∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.

D

WX ≅ ZY by definition of a parallelogram.

E

WZ ≅ XY by the given.

1

Given: RW ≅ WT; UW ≅ WS

Answers:

♣ =:vertical angles theorem

♦ =:SAS

♠ =:CPCTC

2

✔ SASASACPCTC

A

✔ SAS

B

ASA

C

CPCTC

3

✔ CPCTCSASASA

A

✔ CPCTC

B

SAS

C

ASA

115530

⇒ 3

Answer:

115530

115534

⇒ 105

Answer:

115534

115535

✔ ONMMNONOM

Answers:

Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △. By CPCTC, ∠LMO ≅ :ONM

Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △. By CPCTC, ∠LMO ≅ :NOM

Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △. By CPCTC, ∠LMO ≅ :alternate interior angles

115535

Given: RW ≅ WT; UW ≅ WS

Answers:

Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △. By CPCTC, ∠LMO ≅ :ONM

Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △. By CPCTC, ∠LMO ≅ :NOM

Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △. By CPCTC, ∠LMO ≅ :alternate interior angles

115536

✔ NOMMNOONM

A

✔ NOM

B

MNO

C

ONM

115537

✔ alternate interior anglesalternate exterior anglescorresponding angles

A

✔ alternate interior angles

B

alternate exterior angles

C

corresponding angles

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