AnswersCR CCSS Math 2 S2 M2960OXProving a Quadrilateral Is a Parallelogram

Special Parallelograms Answers

19 verified answers3 views
2
Free Preview

⇒ 34

Answer:

115706

3

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.
4

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

Answers:
♣ =:parallelogram side theorem
♦ =:SAS
♠ =:CPCTC
5

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
6

45✔ 5190102

A
45
B
✔ 51
C
90
D
102
7

5✔ 1025102

A
5
B
✔ 10
C
25
D
102
8

✔ 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
9

symmetric propertyaddition property✔ reflexive property

A
symmetric property
B
addition property
C
✔ reflexive property
10

ADAB✔ BE

A
AD
B
AB
C
✔ BE
11

✔ SSSSASAAS

A
✔ SSS
B
SAS
C
AAS
12

definition of right angles✔ definition of perpendiculardefinition of diagonal

A
definition of right angles
B
✔ definition of perpendicular
C
definition of diagonal
13

Given: Parallelogram LMNO; MO ⊥ LN

Answers:
♣::All right angles are congruent.
♦::reflexive property
♠::Opposite sides of a parallelogram are congruent.
14

transitive propertysubstitution property✔ reflexive propertysymmetric property

A
transitive property
B
substitution property
C
✔ reflexive property
D
symmetric property
15

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.
16

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.
17

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

Answers:
♣ =:parallelogram side theorem
♦ =:SAS
♠ =:CPCTC
18

✔ SASAASCPCTC

A
✔ SAS
B
AAS
C
CPCTC
19

✔ CPCTCSASAAS

A
✔ CPCTC
B
SAS
C
AAS

Did you find these answers helpful?