Special Parallelograms Answers

1

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Which characteristic guarantees that a parallelogram is a rectangle?

A

All of the sides are congruent.

B

The opposite sides are parallel.

C

The diagonals are perpendicular bisectors.

D

The diagonals are congruent.

1

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Claire is designing a banner that will hang in her classroom. The length of one diagonal of the banner is 48 inches, and the sides are 25 inches long. Is the banner a square?

A

It is not a square because opposite angles are not congruent.

B

It is not a square because the angles at the vertices are not right angles.

C

It is a square because all the sides are congruent.

D

It is a square because the diagonals are perpendicular.

115703

Use the diagram to answer the questions.

Answers:

The length of AB is .:12

The length of BC is .:5

The length of AC is .:13

115704

✔ 5121317

A

✔ 5

B

12

C

13

D

17

115705

512✔ 1317

A

5

B

12

C

✔ 13

D

17

115706

Question text not available

Answer:

34

115707

Use the diagram of rhombus LMNO to find the missing measures.

Answers:

The measure of ∠LPM is °.:90

The measure of ∠PMN is °.:51

The length of LN is units.:10

115708

45✔ 5190102

A

45

B

✔ 51

C

90

D

102

115709

5✔ 1025102

A

5

B

✔ 10

C

25

D

102

115710

✔ ABAEAC

Answers:

We are given that ABCD is a square. If we consider triangle AEB and triangle AED, we see that side is congruent to side AD because sides of a square are congruent. We know that side AE is congruent to:AB

We are given that ABCD is a square. If we consider triangle AEB and triangle AED, we see that side is congruent to side AD because sides of a square are congruent. We know that side AE is congruent to:reflexive property

We are given that ABCD is a square. If we consider triangle AEB and triangle AED, we see that side is congruent to side AD because sides of a square are congruent. We know that side AE is congruent to:BE

We are given that ABCD is a square. If we consider triangle AEB and triangle AED, we see that side is congruent to side AD because sides of a square are congruent. We know that side AE is congruent to:SSS

We are given that ABCD is a square. If we consider triangle AEB and triangle AED, we see that side is congruent to side AD because sides of a square are congruent. We know that side AE is congruent to:definition of perpendicular

115711

symmetric propertyaddition property✔ reflexive property

A

symmetric property

B

addition property

C

✔ reflexive property

115712

ADAB✔ BE

A

AD

B

AB

C

✔ BE

115713

✔ SSSSASAAS

A

✔ SSS

B

SAS

C

AAS

115714

definition of right angles✔ definition of perpendiculardefinition of diagonal

A

definition of right angles

B

✔ definition of perpendicular

C

definition of diagonal

115715

Given: Parallelogram LMNO; MO ⊥ LN

Answers:

♣::All right angles are congruent.

♦::reflexive property

♠::Opposite sides of a parallelogram are congruent.

115716

transitive propertysubstitution property✔ reflexive propertysymmetric property

A

transitive property

B

substitution property

C

✔ reflexive property

D

symmetric property

115717

Opposite angles of a parallelogram are congruent.✔ Opposite sides of a parallelogram are congruent.Diagonals of a parallelogram are congruent.X Diagonals of a parallelogram bisect each other.

A

Opposite angles of a parallelogram are congruent.

B

✔ Opposite sides of a parallelogram are congruent.

C

Diagonals of a parallelogram are congruent.

D

X Diagonals of a parallelogram bisect each other.

115718

Given: ABCD is a rectangle. Prove: ABCD has congruent diagonals.

Answers:

♣ =:parallelogram side theorem

♦ =:SAS

♠ =:CPCTC

115718

Given: ABCD is a rectangle. Prove: ABCD has congruent diagonals.

Answers:

♣ =:parallelogram side theorem

♦ =:SAS

♠ =:CPCTC

115719

✔ SASAASCPCTC

A

✔ SAS

B

AAS

C

CPCTC

115720

✔ CPCTCSASAAS

A

✔ CPCTC

B

SAS

C

AAS

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