Question

for each of the following, determine if $overline{ab}$ is a median, an altitude, a perpendicular bisector, and/or an angle bisector. give a brief explanation to justify your answer.

Explanation:

Step1: Recall definitions

Median: A line - segment joining a vertex of a triangle to the mid - point of the opposite side. Altitude: A line segment from a vertex perpendicular to the opposite side. Perpendicular bisector: A line that is perpendicular to a segment and bisects it. Angle bisector: A line that divides an angle into two equal angles.

Step2: Analyze each triangle

1. Since the marks on the opposite side of vertex A show that the two sub - segments are equal, $\overline{AB}$ is a median.
2. The right - angle symbol indicates that $\overline{AB}$ is perpendicular to the opposite side, so $\overline{AB}$ is an altitude.
3. The right - angle symbol and the equal sub - segments on the opposite side mean $\overline{AB}$ is a perpendicular bisector.
4. The right - angle symbol makes $\overline{AB}$ an altitude.
5. The marks on the opposite side of vertex B show $\overline{AB}$ is a median.
6. The marks on the opposite side of vertex A and the equal angles formed by $\overline{AB}$ with the sides of the vertex A mean $\overline{AB}$ is both a median and an angle bisector.
7. The marks on the opposite side of vertex A show $\overline{AB}$ is a median.
8. The right - angle symbol makes $\overline{AB}$ an altitude.
9. The right - angle symbol makes $\overline{AB}$ an altitude.
10. The equal angles formed by $\overline{AB}$ with the sides of vertex A make $\overline{AB}$ an angle bisector.
11. The right - angle symbol and the equal sub - segments on the opposite side make $\overline{AB}$ a perpendicular bisector.
12. The equal angles formed by $\overline{AB}$ with the sides of vertex A make $\overline{AB}$ an angle bisector.

Answer:

1. Median
2. Altitude
3. Perpendicular bisector
4. Altitude
5. Median
6. Median and angle bisector
7. Median
8. Altitude
9. Altitude
10. Angle bisector
11. Perpendicular bisector
12. Angle bisector