4.6 More Special Segments in a Triangle

1. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Perpendicular Bisector

Angle Bisector

Median

Altitude

The given picture and markings do not provide enough information to determine if the dotted line is a perpendicular bisector, a median, or an altitude. However, based on the markings, it can be inferred that the dotted line is an angle bisector.

Explanation

The given picture and markings do not provide enough information to determine if the dotted line is a perpendicular bisector, a median, or an altitude. However, based on the markings, it can be inferred that the dotted line is an angle bisector.

2. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Median

Angle Bisector

Altitude

The given picture and markings indicate that the dotted line is a median. In a triangle, a median is a line segment that connects a vertex to the midpoint of the opposite side. It divides the opposite side into two equal segments.

Explanation

The given picture and markings indicate that the dotted line is a median. In a triangle, a median is a line segment that connects a vertex to the midpoint of the opposite side. It divides the opposite side into two equal segments.

3. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Median

Angle Bisector

Altitude

The correct answer is Median. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In the given picture, the dotted line connects a vertex of the triangle to the midpoint of the opposite side, which is the definition of a median. Therefore, the dotted line represents a median.

Explanation

The correct answer is Median. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In the given picture, the dotted line connects a vertex of the triangle to the midpoint of the opposite side, which is the definition of a median. Therefore, the dotted line represents a median.

4. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Perpendicular Bisector

Angle Bisector

Altitude

The correct answer is "Perpendicular Bisector" because a perpendicular bisector is a line that divides a line segment into two equal parts at a right angle. In the given picture, the dotted line is shown dividing the line segment into two equal parts, and it is perpendicular to the line segment. Therefore, it can be identified as a perpendicular bisector.

Explanation

The correct answer is "Perpendicular Bisector" because a perpendicular bisector is a line that divides a line segment into two equal parts at a right angle. In the given picture, the dotted line is shown dividing the line segment into two equal parts, and it is perpendicular to the line segment. Therefore, it can be identified as a perpendicular bisector.

5. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Altitude

Perpendicular Bisector

Median

The correct answer is "Altitude". In the given picture, the dotted line is perpendicular to the base of the triangle and passes through one of the vertices. This is the definition of an altitude in a triangle.

Explanation

The correct answer is "Altitude". In the given picture, the dotted line is perpendicular to the base of the triangle and passes through one of the vertices. This is the definition of an altitude in a triangle.

6.

Median x = 1

Median x = 10

Median x = 7

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Explanation

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7.

Angle Bisector x = 15

Angle Bisector x = 13

Angle Bisector x = 10

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Explanation

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8. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Median

Angle Bisector

Altitude

The given answer is "Angle Bisector" because an angle bisector is a line that divides an angle into two equal parts. In the given picture, the dotted line appears to be dividing the angle formed by the two lines into two equal parts, indicating that it is an angle bisector.

Explanation

The given answer is "Angle Bisector" because an angle bisector is a line that divides an angle into two equal parts. In the given picture, the dotted line appears to be dividing the angle formed by the two lines into two equal parts, indicating that it is an angle bisector.

9.

N = 8

N = 6

N = 5

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Explanation

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10. Given the following picture and markings, identify if the dotted line is an angle bisector, a perpendicular bisector, an altitude, a misegment or a median. Choose the one that best represents the dotted line.

Perpendicular Bisector

Altitude

Median

Midsegment

The dotted line in the picture is best represented as a midsegment. A midsegment is a line segment that connects the midpoints of two sides of a triangle. In the given picture, the dotted line appears to connect the midpoints of two sides of a triangle, making it a midsegment.

Explanation

The dotted line in the picture is best represented as a midsegment. A midsegment is a line segment that connects the midpoints of two sides of a triangle. In the given picture, the dotted line appears to connect the midpoints of two sides of a triangle, making it a midsegment.