Asked by confusion manual

If lines s and t are parallel, which pair of angles is supplementary and why?

(1 point)
Responses

∠B
and ∠G
because they are consecutive interior angles
∠B
and ∠G
because they are consecutive interior angles

∠G
and ∠D
because they are a linear pair
∠G
and ∠D
because they are a linear pair

∠A
and ∠B
because they are corresponding angles
∠A
and ∠B
because they are corresponding angles

∠A
and ∠D
because they are consecutive exterior angles
Answered by confusion manual
Use the image to answer the question.

A horizontal line is intersected by two parallel lines lower s and lower t that slant from left to right forming eight angles.

If lines s and t are parallel, which pair of angles is supplementary and why?

(1 point)
Responses

∠B
and ∠G
because they are consecutive interior angles
∠B
and ∠G
because they are consecutive interior angles

∠G
and ∠D
because they are a linear pair
∠G
and ∠D
because they are a linear pair

∠A
and ∠B
because they are corresponding angles
∠A
and ∠B
because they are corresponding angles

∠A
and ∠D
because they are consecutive exterior angles
∠A
and ∠D
because they are consecutive exterior angles
Answered by confusion manual
Use the image to answer the question.

A vertical line is intersected by two parallel lines lower m and lower n forming eight angles.

Lines m and n are parallel. Angle E
measures (3x+18)
degrees and angle B
measures (14x−8)
degrees. What is the value of x?

(1 point)
Responses

132

48

Start Fraction 26 over 11 End Fraction

10


Answered by confusion manual
Line segment AC¯¯¯¯¯¯¯¯
is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯
, with the two segments meeting at point E
. What is true of segment BE¯¯¯¯¯¯¯¯
? (1 point)
Responses

It must be the same length as segment BC¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper B upper C .

It must be the same length as segment DE¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper D upper E .

It must be the same length as segment EA¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper C upper D .

It must be the same length as segment AB¯¯¯¯¯¯¯¯
.
Answered by confusion manual
Lenny wrote a paragraph proof of the Perpendicular Bisector Theorem. What mistake did Lenny make in his proof?

HK¯¯¯¯¯¯¯¯¯
is a perpendicular bisector of IJ¯¯¯¯¯¯
, and L is the midpoint of IJ¯¯¯¯¯¯
. M is a point on the perpendicular bisector, HK¯¯¯¯¯¯¯¯¯
. By the definition of a perpendicular bisector, I know that IM¯¯¯¯¯¯¯¯≅JM¯¯¯¯¯¯¯¯
. By the definition of a perpendicular bisector, I also know that ∠MLI
and ∠MLJ
are right angles. ∠MLI≅∠MLJ
because of the Right Angle Congruence Theorem. I can also say that ML¯¯¯¯¯¯¯¯¯≅ML¯¯¯¯¯¯¯¯¯
by the Reflexive Property of Congruence. With this information, I know that △MLI≅△MLJ
by the SAS Congruence Theorem. Since the triangles are congruent, the CPCTC Theorem allows me to know that IL¯¯¯¯¯¯≅JL¯¯¯¯¯¯¯
. Knowing that these segments are congruent proves the Perpendicular Bisector Theorem.

(1 point)
Responses

The definition of a perpendicular bisector tells you that∠LMI
and ∠LMJ
are right angles, not that ∠MLI
and ∠MLJ
are right angles.
The definition of a perpendicular bisector tells you that ∠LMI
and ∠LMJ
are right angles, not that ∠MLI
and ∠MLJ
are right angles.

The definition of a perpendicular bisector tells you that IL¯¯¯¯¯¯≅JL¯¯¯¯¯¯¯
, not that IM¯¯¯¯¯¯¯¯≅JM¯¯¯¯¯¯¯¯
.
The definition of a perpendicular bisector tells you that line segment cap i liters is congruent to line segment cap j liters, not that line segment cap i cap m is congruent to line segment cap j cap m.

Lenny did not make a mistake. His proof is correct.
Lenny did not make a mistake. His proof is correct.

The SAS Congruence Theorem tells you that △MLI≅△JLM
, not that △MLI≅△MLJ
.
The SAS Congruence Theorem tells you that △MLI≅△JLM
, not that △MLI≅△MLJ
.
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Answered by confusion manual
¯¯¯¯¯
is a perpendicular bisector of KM¯¯¯¯¯¯¯¯¯¯
. Hallie locates point H
along line segment JL¯¯¯¯¯¯¯
. If the length of KH¯¯¯¯¯¯¯¯¯
is given by 6y+3
and the length of HM¯¯¯¯¯¯¯¯¯¯
is given by 2y+7
, what is the length in units of segment HM¯¯¯¯¯¯¯¯¯¯
? (1 point)
Responses

1
1

8
8

9
9

18
Answered by confusion manual
JL¯¯¯¯¯¯¯
is a perpendicular bisector of KM¯¯¯¯¯¯¯¯¯¯
. Hallie locates point H
along line segment JL¯¯¯¯¯¯¯
. If the length of KH¯¯¯¯¯¯¯¯¯
is given by 6y+3
and the length of HM¯¯¯¯¯¯¯¯¯¯
is given by 2y+7
, what is the length in units of segment HM¯¯¯¯¯¯¯¯¯¯
? (1 point)
Responses

1

8

9

18
Answered by confusion manual
Use the image to answer the question.

An image is shown of perpendicular bisector VZ intersecting line segment WY at point X. Point U is a point on the perpendicular bisector.

Harriet has written a proof to prove that point U is equidistant from points W and Y. She knows that ZV¯¯¯¯¯¯¯¯
is the perpendicular bisector of WY¯¯¯¯¯¯¯¯¯
.

Statement Reason
1. ZV¯¯¯¯¯¯¯¯
is the perpendicular bisector of WY¯¯¯¯¯¯¯¯¯
. given
2. WX¯¯¯¯¯¯¯¯¯¯≅YX¯¯¯¯¯¯¯¯
definition of a perpendicular bisector
3. ∠WXU
and ∠YXU
are right angles. definition of a perpendicular bisector
4. ∠WXU≅∠YXU
Right Angle Congruence Theorem
5. XU¯¯¯¯¯¯¯¯≅XU¯¯¯¯¯¯¯¯
Reflexive Property of Congruence
6. UW¯¯¯¯¯¯¯¯¯≅UY¯¯¯¯¯¯¯¯
CPCTC Theorem

What is the missing step in her proof?

Option 1: There is no missing step in Harriet's proof.

Option 2: Harriet forgot the step where she proves that ∠XUW≅∠XUY
because of the CPCTC Theorem.

Option 3: Harriet forgot the step where she proves that △WXU≅△YXU
because of the SAS Congruence Theorem.

(1 point)
The missing statement in Harriet's proof is ?
Answered by confusion manual
Use the image to answer the question.

The outline of a kite is in the shape of a diamond. The vertices of this diamond are labeled upper F, upper G, upper K, and upper J, respectively. Each of these points are connected via lines that intersect at a central, interior point: upper H.

In quadrilateral FGKJ
, FK¯¯¯¯¯¯¯¯
is a perpendicular bisector of GJ¯¯¯¯¯¯¯
. The length of segment GF¯¯¯¯¯¯¯¯
is 6+x
units, and the length of segment JF¯¯¯¯¯¯¯
is 3x−5
units. What is the value of x?

(1 point)
The value of x is
.
Remaining Attempts : 3
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Answered by GPT 3.5
∠G and ∠D because they are a linear pair. When two parallel lines are intersected by a transversal, alternate interior angles are congruent. Since ∠G and ∠D are alternate interior angles, they are congruent and form a linear pair, which means they are supplementary.
Answered by GPT 3.5
Based on the given information and the image, the correct answer is:

∠G and ∠D because they are a linear pair.
Answered by GPT 3.5
To find the value of x, we can set the measures of the two angles equal to each other and solve for x.

3x + 18 = 14x - 8

Combine like terms:

8 + 18 = 14x - 3x

26 = 11x

Divide both sides by 11:

x = 26/11

Therefore, the value of x is Start Fraction 26 over 11 End Fraction.
Answered by GPT 3.5
It must be the same length as segment AB¯¯¯¯¯¯¯¯.

Since segment AC¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯, point E is the midpoint of segment BD¯¯¯¯¯¯¯¯. This means that segment BE¯¯¯¯¯¯¯¯ is equal in length to segment AB¯¯¯¯¯¯¯¯, as they both connect to the midpoint E.
Answered by GPT 3.5
The mistake that Lenny made in his proof is:

The definition of a perpendicular bisector tells you that ∠LMI and ∠LMJ are right angles, not that ∠MLI and ∠MLJ are right angles.

Lenny mistakenly wrote ∠MLI and ∠MLJ as the right angles formed by the perpendicular bisector, while it should be ∠LMI and ∠LMJ.
Answered by GPT 3.5
To find the length of segment HM¯¯¯¯¯¯¯¯¯¯, we can substitute the given expressions for KH¯¯¯¯¯¯¯¯¯ and HM¯¯¯¯¯¯¯¯¯¯ into the expression for segment KM¯¯¯¯¯¯¯¯¯¯:

KM¯¯¯¯¯¯¯¯¯¯ = KH¯¯¯¯¯¯¯¯¯ + HM¯¯¯¯¯¯¯¯¯¯

6y + 3 + 2y + 7 = HM¯¯¯¯¯¯¯¯¯¯

Combine like terms:

8y + 10 = HM¯¯¯¯¯¯¯¯¯¯

Therefore, the length of segment HM¯¯¯¯¯¯¯¯¯¯ is given by the expression 8y + 10.
Answered by GPT 3.5
To find the length of segment HM¯¯¯¯¯¯¯¯¯¯, we need to find the value of y and then substitute it into the expression 2y + 7.

Since JL¯¯¯¯¯¯¯ is a perpendicular bisector of KM¯¯¯¯¯¯¯¯¯¯, we know that KH¯¯¯¯¯¯¯¯¯ and HM¯¯¯¯¯¯¯¯¯¯ are congruent. Therefore, we can set the expressions for their lengths equal to each other:

6y + 3 = 2y + 7

Subtract 2y from both sides:

4y + 3 = 7

Subtract 3 from both sides:

4y = 4

Divide both sides by 4:

y = 1

Now we can substitute y = 1 into the expression 2y + 7 to find the length of segment HM¯¯¯¯¯¯¯¯¯¯:

2(1) + 7 = 2 + 7 = 9

Therefore, the length of segment HM¯¯¯¯¯¯¯¯¯¯ is 9 units.
Answered by GPT 3.5
The missing statement in Harriet's proof is:

Option 3: Harriet forgot the step where she proves that △WXU≅△YXU because of the SAS Congruence Theorem.
Answered by GPT 3.5
To find the value of x, we can set the lengths of segment GF¯¯¯¯¯¯¯¯ and segment JF¯¯¯¯¯¯¯ equal to each other and solve for x.

GF¯¯¯¯¯¯¯¯ = JF¯¯¯¯¯¯¯

6 + x = 3x - 5

Combine like terms:

5 + x = 3x - 6

Add 6 to both sides:

11 + x = 3x

Subtract x from both sides:

11 = 2x

Divide both sides by 2 to solve for x:

x = 5.5

Therefore, the value of x is 5.5.