Question

У трикутнику DEF проведено відрізок ЕА. Визначте, чи є цей відрізок медіаною, бісектрисою або висотою даного трикутника, якщо: AF = DA=4см; DAE = FAE =90º ; DEA = FEA = 30º.

Answer 1

Given Information:

- Triangle DEF - Segment EA is drawn in triangle DEF - AF = DA = 4 cm - DAE = FAE = 90º - DEA = FEA = 30º

Analysis:

To determine whether segment EA is a median, bisector, or altitude of triangle DEF, we need to understand the definitions of these terms:

- Median: A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. - Bisector: A bisector of a triangle is a line segment that divides an angle into two equal angles. - Altitude: An altitude of a triangle is a line segment that is perpendicular to a side and passes through the opposite vertex.

Solution:

To determine the nature of segment EA, we will analyze the given information.

1. Median: To check if EA is a median, we need to verify if it connects a vertex to the midpoint of the opposite side. However, we do not have any information about the midpoint of the opposite side, so we cannot determine if EA is a median.

2. Bisector: To check if EA is a bisector, we need to verify if it divides an angle into two equal angles. In this case, we have two angles, DAE and FAE, both of which are 90º. Since EA does not divide these angles into two equal angles, we can conclude that EA is not a bisector.

3. Altitude: To check if EA is an altitude, we need to verify if it is perpendicular to a side and passes through the opposite vertex. In this case, we have two angles, DEA and FEA, both of which are 30º. Since EA is not perpendicular to either side DE or EF, we can conclude that EA is not an altitude.

Based on the given information, we can determine that segment EA is neither a median, bisector, nor altitude of triangle DEF.

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