4.6 PreAP Special Segments

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| By Blinda Windham

Blinda Windham

Community Contributor

Quizzes Created: 9 | Total Attempts: 1,730

Questions: 11 | Attempts: 103 | Updated: Feb 28, 2024

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Segements in a Triangle and Coordinate Graphing

Questions and Answers

1.

1. Which of the following choices BEST describes the special segment UT?
- A.
  
  Altitude
- B.
  
  Median
- C.
  
  Perpendicular Bisector
- D.
  
  Angle Bisector
Correct Answer
C. Perpendicular Bisector

Explanation
BEST describes means the answer describes the line in the best possible way.

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2.

2. Which of the following BEST describes the special segment UT?
- A.
  
  Median
- B.
  
  Altitude
- C.
  
  Perpendicular Bisector
- D.
  
  Angle Bisector
Correct Answer
D. Angle Bisector

Explanation
The special segment UT is an angle bisector. An angle bisector is a line or ray that divides an angle into two congruent angles. In this case, the segment UT divides an angle into two equal angles, making it an angle bisector.

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3.

Which of the following BEST describes the special segment UT?
- A.
  
  Median
- B.
  
  Altitude
- C.
  
  Perpendicular Bisector
- D.
  
  Angle Bisector
Correct Answer
B. Altitude

Explanation
An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. It is used to find the height or distance between the vertex and the opposite side. In this case, the special segment UT is described as an altitude, indicating that it is a line segment drawn from vertex U perpendicular to the opposite side T.

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4.

Which of the following BEST describes the special segment UT?
- A.
  
  Median
- B.
  
  Altitude
- C.
  
  Perpendicular Bisector
- D.
  
  Angle Bisector
Correct Answer
A. Median

Explanation
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. In the context of the question, the special segment UT is described as a median because it connects a vertex U to the midpoint T of the opposite side.

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5.

Draw the altitude from point G. What is the slope of the altitude?
- A.
  
  8/4 or 2/1
- B.
  
  -4/8 or -1/2
- C.
  
  7/3
- D.
  
  6/8 or 3/4
Correct Answer
B. -4/8 or -1/2

Explanation
The slope of the altitude from point G can be determined by finding the slope of the line passing through point G and the orthocenter of the triangle. Since the orthocenter is the intersection of the altitudes, the slope of the altitude is the negative reciprocal of the slope of the line passing through the orthocenter and the midpoint of the opposite side. In this case, the slope is -1/2 or -4/8.

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6.

Draw the altitude from point Q. What is the slope of the altitude?
- A.
  
  6/9 or 2/3
- B.
  
  -6/9 or -2/3
- C.
  
  9/6 or 3/2
- D.
  
  -9/6 or -3/2
Correct Answer
A. 6/9 or 2/3
7.

True or False. Find the point of concurrency of the perpendicular bisectors. The point of concurrency is on the hypotenuse of the triangle.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The point of concurrency of the perpendicular bisectors is called the circumcenter of the triangle. It is the center of the circle that passes through all three vertices of the triangle. Since the hypotenuse is one of the sides of the triangle, the circumcenter must lie on it. Therefore, the statement is true.

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8.

True or False. Find the point of concurrency of the altitudes. The point of concurrency is inside the triangle.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The point of concurrency of the altitudes is at the 90 degree angle.

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