# The bisectors of the angles A and D of the parallelogram ABCD intersect at a point lying on the side BC. Find AB if BC = 40

BC || AD (by definition of parallelogram)
∠BAE = ∠EAD (since AE is a bisector)
∠EAD = ∠BEA (as these are cross-angles)
Therefore, ∠BAE = ∠BEA
It turns out that the triangle ABE is an isosceles (by property), and AB = BE (by the definition of an isosceles triangle).
Similarly with the triangle ECD:
∠CED = ∠CDE
EC = CD
Since AB = CD (by the parallelogram property), it turns out that AB = BE = EC = CD.
Therefore, BE = BC / 2 = 40/2 = 20.
AB = BE = 20
Answer: AB = 20

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}