Question

Use the image to answer the question.

A parallelogram has its vertices labeled upper A upper B upper C upper D. Two sets of opposite sides are marked as congruent.

Prove that quadrilateral ABCD
is a parallelogram. How do you know that the figure is a parallelogram?

(1 point)
Responses

Adjacent sides of the figure are congruent.
Adjacent sides of the figure are congruent.

Opposite sides of the figure are congruent.
Opposite sides of the figure are congruent.

Adjacent sides of the figure are parallel.
Adjacent sides of the figure are parallel.

Adjacent angles of the figure are congruent.
Adjacent angles of the figure are congruent.
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Question
Edwidge draws parallelogram STUV
with a center at O
. What must be true to prove that STUV
is a parallelogram?(1 point)
Responses

ST¯¯¯¯¯¯¯≅UV¯¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯
line segment cap s cap t is congruent to line segment cap u cap v A n d line segment cap t cap u comma line segment cap u cap v and line segment cap t cap u is congruent to line segment cap s cap v

SO¯¯¯¯¯¯¯≅TO¯¯¯¯¯¯¯ and UO¯¯¯¯¯¯¯¯ ≅VO¯¯¯¯¯¯¯¯
line segment cap s cap o is congruent to line segment cap t cap o A n d line segment cap u cap o comma line segment cap t cap o and line segment cap u cap o is congruent to line segment cap v cap o

ST¯¯¯¯¯¯¯≅TU¯¯¯¯¯¯¯ and UV¯¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯
line segment cap s cap t is congruent to line segment cap t cap u A n d line segment cap u cap v comma line segment cap t cap u and line segment cap u cap v is congruent to line segment cap s cap v

SO¯¯¯¯¯¯¯≅VO¯¯¯¯¯¯¯¯ and TO¯¯¯¯¯¯¯ ≅UO¯¯¯¯¯¯¯¯
line segment cap s cap o is congruent to line segment cap v cap o and line segment cap t cap o comma line segment cap v cap o A n d line segment cap t cap o is congruent to line segment cap u cap o
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Question
Use the image to answer the question.

A parallelogram has vertices upper A, upper B, upper C, and upper D. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper O. The lines formed between each vertex and upper O are labeled.

To prove that quadrilateral ABCD
is a parallelogram, what must be the value of m?

(1 point)
Responses

15
15

36
36

11
11

18
Question
Use the image to answer the question.

A parallelogram has vertices upper Q, upper R, upper S, and upper T. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper P. Sides upper Q upper R and upper T upper S are much longer than the other sides.

It is given that quadrilateral QRST
is a parallelogram. Which segment of the figure must be congruent to segment SP¯¯¯¯¯¯¯
?

(1 point)
Responses

PR¯¯¯¯¯¯¯¯
upper P upper R

QS¯¯¯¯¯¯¯
upper Q upper S

QP¯¯¯¯¯¯¯¯
upper Q upper P

PT¯¯¯¯¯¯¯
upper P upper T
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Use the image to answer the question.

A parallelogram has vertices upper A, upper B, upper C, and upper D. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper E. Sides upper A upper D and upper B upper C are much longer than the other sides.

If you were to prove that quadrilateral ABCD
is a parallelogram, what would need to be true about EB
and ED
?

(1 point)
Responses

ED ¯¯¯¯¯¯¯¯¯ must be half of the length of EB¯¯¯¯¯¯¯¯.
ED ¯¯¯¯¯¯¯¯¯ must be half of the length of EB¯¯¯¯¯¯¯¯.

EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯.
EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯.

EB ¯¯¯¯¯¯¯¯¯ must be half of the length of ED¯¯¯¯¯¯¯¯.
EB ¯¯¯¯¯¯¯¯¯ must be half of the length of ED¯¯¯¯¯¯¯¯.

ED ¯¯¯¯¯¯¯¯¯ must be a different length than EB.¯¯¯¯¯¯¯¯¯
ED ¯¯¯¯¯¯¯¯¯ must be a different length than EB.¯¯¯¯¯¯¯¯¯
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Answer 1

Here are the answers:

1) How do you know ABCD is a parallelogram?
- Opposite sides of the figure are congruent.

2) Edwidge draws parallelogram STUV with center O. What must be true?
- SO ≅ TO and UO ≅ VO (the diagonals are bisected at O).

3) To prove ABCD is a parallelogram, what must be the value of m?
- I can’t determine m without the labels/expressions on the diagonal segments in the image. The rule to use: diagonals bisect each other, so set the two segment expressions equal and solve for m. Please provide the segment expressions or re-upload the image.

4) In parallelogram QRST (diagonals intersect at P), which segment is congruent to SP?
- QP

5) For parallelogram ABCD with diagonals intersecting at E, what must be true about EB and ED?
- EB must be the same length as ED (E is the midpoint of BD).