5.3 Medians and Altitudes Geo - Lauren Crongeyer | Library | Formative - Free Printable

Problem Analysis:

The task involves identifying the type of segment in each given triangle. The segments can be classified as one of the following:
1. Perpendicular Bisector: A line segment that is perpendicular to a side of the triangle and passes through its midpoint.
2. Angle Bisector: A line segment that divides an angle of the triangle into two equal angles.
3. Altitude: A line segment drawn from a vertex of the triangle perpendicular to the opposite side (or its extension).
4. Median: A line segment drawn from a vertex of the triangle to the midpoint of the opposite side.
5. None of these: If the segment does not fit any of the above definitions.

We will analyze each figure step by step.

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Part 1: Classify Each Segment in Figures 1–6

#### Figure 1:
- Description: A line segment \( \overline{AB} \) is drawn from a vertex perpendicular to the opposite side.
- Classification: This is an altitude because it is perpendicular to the base and extends from a vertex.

#### Figure 2:
- Description: A line segment \( \overline{AB} \) bisects an angle of the triangle.
- Classification: This is an angle bisector because it divides the angle into two equal parts.

#### Figure 3:
- Description: A line segment \( \overline{AB} \) connects a vertex to the midpoint of the opposite side.
- Classification: This is a median because it connects a vertex to the midpoint of the opposite side.

#### Figure 4:
- Description: A line segment \( \overline{AB} \) is perpendicular to a side and passes through its midpoint.
- Classification: This is a perpendicular bisector because it is perpendicular to the side and bisects it.

#### Figure 5:
- Description: A line segment \( \overline{AB} \) is drawn from a vertex perpendicular to the opposite side.
- Classification: This is an altitude because it is perpendicular to the base and extends from a vertex.

#### Figure 6:
- Description: A line segment \( \overline{AB} \) connects a vertex to the midpoint of the opposite side.
- Classification: This is a median because it connects a vertex to the midpoint of the opposite side.

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Part 2: Classify Each Segment in Figures 7–16

#### Figure 7:
- Description: A line segment is drawn from a vertex perpendicular to the opposite side.
- Classification: Altitude

#### Figure 8:
- Description: A line segment bisects an angle of the triangle.
- Classification: Angle Bisector

#### Figure 9:
- Description: A line segment connects a vertex to the midpoint of the opposite side.
- Classification: Median

#### Figure 10:
- Description: A line segment is perpendicular to a side and passes through its midpoint.
- Classification: Perpendicular Bisector

#### Figure 11:
- Description: A line segment is drawn from a vertex perpendicular to the opposite side.
- Classification: Altitude

#### Figure 12:
- Description: A line segment connects a vertex to the midpoint of the opposite side.
- Classification: Median

#### Figure 13:
- Description: A line segment bisects an angle of the triangle.
- Classification: Angle Bisector

#### Figure 14:
- Description: A line segment is perpendicular to a side and passes through its midpoint.
- Classification: Perpendicular Bisector

#### Figure 15:
- Description: A line segment is drawn from a vertex perpendicular to the opposite side.
- Classification: Altitude

#### Figure 16:
- Description: A line segment connects a vertex to the midpoint of the opposite side.
- Classification: Median

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Final Answer:

Summarizing the classifications for all figures:

1. Altitude
2. Angle Bisector
3. Median
4. Perpendicular Bisector
5. Altitude
6. Median
7. Altitude
8. Angle Bisector
9. Median
10. Perpendicular Bisector
11. Altitude
12. Median
13. Angle Bisector
14. Perpendicular Bisector
15. Altitude
16. Median

$$
\boxed{\text{See detailed classifications above}}
$$