The median, drawn from angle B of triangle ABC, intersects the base AC at point D and, stretching from point D

| September 8, 2021 | education

The median, drawn from angle B of triangle ABC, intersects the base AC at point D and, stretching from point D to point E in the opposite direction, will cut off the segments DE = BD. Find angle BAE if angle BAD = 56 ° and angle angle BCD = 40 °

1. The segment BD is equal to the segment ED (by condition),

2. The segment CD is equal to the segment AD (BD is the median),

Therefore, the quadrilateral ABCE is a parallelogram (by the property of the parallelogram diagonals).

This means that straight lines BC and AE are parallel.

Consider the angles BCD and EAD: straight line BC is parallel to AE (by the property of a parallelogram), AC is a secant (intersects both straight lines), so the angle BCD = EAD = 40 degrees.

The angle BAE is equal to the sum of the angles BAD and EAD, so the angle BAE = 40 + 56 = 96 degrees.

Answer: The angle BAE is 96 degrees.



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