Special Parallelograms Answers

22 verified answers3 views
3

512✔ 1317

A
5
B
12
C
✔ 13
D
17
4

✔ SSSSASAAS

A
✔ SSS
B
SAS
C
AAS
5

definition of right angles✔ definition of perpendiculardefinition of diagonal

A
definition of right angles
B
✔ definition of perpendicular
C
definition of diagonal
6

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
8

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.
9

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
10

✔ 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
11

45✔ 5190102

A
45
B
✔ 51
C
90
D
102
12

symmetric propertyaddition property✔ reflexive property

A
symmetric property
B
addition property
C
✔ reflexive property
13

5✔ 1025102

A
5
B
✔ 10
C
25
D
102
14

ADAB✔ BE

A
AD
B
AB
C
✔ BE
15

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

Answers:
♣ =:parallelogram side theorem
♦ =:SAS
♠ =:CPCTC
16

Given: Parallelogram LMNO; MO ⊥ LN

Answers:
♣::All right angles are congruent.
♦::reflexive property
♠::Opposite sides of a parallelogram are congruent.
17

transitive propertysubstitution property✔ reflexive propertysymmetric property

A
transitive property
B
substitution property
C
✔ reflexive property
D
symmetric property
18

Opposite angles of a parallelogram are congruent.✔ Opposite sides of a parallelogram are congruent.Diagonals of a parallelogram are congruent.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
Diagonals of a parallelogram bisect each other.
19

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.
20

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

Answers:
♣ =:parallelogram side theorem
♦ =:SAS
♠ =:CPCTC

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