4.5 Special Segments In A Triangle Assignment

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| Written by Blinda Windham

Blinda Windham

Community Contributor

Quizzes Created: 10 | Total Attempts: 1,808

Questions: 11 | Attempts: 198 | Updated: Mar 19, 2023

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Segments in A Triangle

Questions and Answers

1.

1. Identify segment UT in the triangle below.
- A.
  
  Perpendicular Bisector
- B.
  
  Altitude
- C.
  
  Median
- D.
  
  Midsegment
Correct Answer
A. Perpendicular Bisector

Explanation
A perpendicular bisector is a line that divides a line segment into two equal parts and is perpendicular to that line segment. In the given triangle, segment UT is a line that divides the line segment UV into two equal parts and is perpendicular to it. Therefore, the correct answer is "Perpendicular Bisector".

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2.

Identify segment UT in the picture below.
- A.
  
  Perpendicular Bisector
- B.
  
  Altitude
- C.
  
  Median
- D.
  
  Midsegment
Correct Answer
B. Altitude

Explanation
The segment UT in the picture is an altitude. An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. In this case, the segment UT is drawn from vertex U and is perpendicular to the side that contains points S and R.

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3.

Identify the special segment UT in the picture below.
- A.
  
  Perpendicular Bisector
- B.
  
  Altitude
- C.
  
  Angle Bisector
- D.
  
  Median
Correct Answer
C. Angle Bisector

Explanation
The special segment UT in the picture is an angle bisector. An angle bisector is a line or segment that divides an angle into two equal parts. In the given picture, UT is dividing the angle formed by the two lines into two equal angles.

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4.

Identify the special segment UT in the picture below.
- A.
  
  Perpendicular Bisector
- B.
  
  Angle Bisector
- C.
  
  Median
- D.
  
  Altitude
Correct Answer
C. Median

Explanation
The special segment UT in the picture is a median. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In this case, UT connects the vertex U to the midpoint of the side ST. Medians have the property that they divide the triangle into two equal areas, and they intersect at a point called the centroid.

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5.

Identfy the special segment UT in the picture below.
- A.
  
  Perpendicular Bisector
- B.
  
  Midsegment
- C.
  
  Median
- D.
  
  Altitude
Correct Answer
B. Midsegment

Explanation
The special segment UT in the picture is the midsegment. The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle. In this case, UT connects the midpoints of two sides of the triangle in the picture. The midsegment is always parallel to the third side of the triangle and is half the length of the third side.

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6.

4.5 problem 8 Check all that apply to the problem. 1. What is the name of the special segment GA? 2. What is the first step to solve for x?
- A.
  
  Median
- B.
  
  Angle Bisector
- C.
  
  3x + 9 = 45
- D.
  
  2(3x + 9) = 45
Correct Answer(s)
B. Angle Bisector
C. 3x + 9 = 45

Explanation
The given correct answer includes two options: "Angle Bisector" and "3x + 9 = 45." The question is asking for all the options that apply to the problem. Therefore, the explanation is that the special segment GA is an angle bisector, and the equation 3x + 9 = 45 is the first step to solve for x.

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7.

4.5 problem 9 If NB = 46, What is the name of the special segment MK and what is the length of MK?
- A.
  
  Midsegment and MK = 23
- B.
  
  Median and MK = 23
- C.
  
  Altitude and MK = 46
- D.
  
  Midsegment and MK = 46
Correct Answer
A. Midsegment and MK = 23

Explanation
The name of the special segment MK is the midsegment, and its length is 23.

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8.

4.5 problem 10. What is the special name of line m and what is the value of x?
- A.
  
  Midsegment; x=18.5
- B.
  
  Perpendicular Bisector; x=18.5
- C.
  
  Median; x=7.5
- D.
  
  Perpendicular Bisector; x=7.5
Correct Answer
D. Perpendicular Bisector; x=7.5

Explanation
The special name of line m is a Perpendicular Bisector. The value of x is 7.5.

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9.

4.5 problem 11. Given altitude OM, what is the value of x?
- A.
  
  X = 10 or -6
- B.
  
  X = -10 or 6
- C.
  
  X = 10 or 6
- D.
  
  X = -10 or -6
Correct Answer
A. X = 10 or -6

Explanation
The given answer states that the value of x can be either 10 or -6. This means that there are two possible values for x that satisfy the given conditions. It is possible that x is equal to 10 or it could be equal to -6.

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10.

4.5 problem 6. What is the name of the special segment AC?
- A.
  
  Median
- B.
  
  Altitude
- C.
  
  Perpendicular Bisector
- D.
  
  All of the above
Correct Answer
A. Median

Explanation
The special segment AC is called a median. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. It divides the triangle into two equal areas and is also the line of symmetry for the triangle.

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11.

4.5 problem 7. What is the name of the special segment SA?
- A.
  
  Altitude
- B.
  
  Median
- C.
  
  Perpendicular Bisector
- D.
  
  All of the Above
Correct Answer
D. All of the Above

Explanation
The special segment SA can be any of the three options: altitude, median, or perpendicular bisector. An altitude is a segment from a vertex of a triangle to the opposite side, a median is a segment from a vertex to the midpoint of the opposite side, and a perpendicular bisector is a segment that cuts a side of a triangle into two equal parts at a right angle. Therefore, all of these options can be the name of the special segment SA.

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