In square ABCD, am intersects BC at m, an intersects DC at n. angle man is 45 degrees. Angle man rotates clockwise around a, and its two sides intersect CB and DC at m respectively In square ABCD, am intersects BC at point m, an intersects DC at point n. angle man is 45 degrees. Angle man rotates clockwise around point a, and its two sides intersect CB and DC at point m and N respectively. When angle man rotates around point a to BM = DN, it is easy to prove BM + DN = Mn. When angle man rotates around point a to BM not = DN, what is the relationship between them?

In square ABCD, am intersects BC at m, an intersects DC at n. angle man is 45 degrees. Angle man rotates clockwise around a, and its two sides intersect CB and DC at m respectively In square ABCD, am intersects BC at point m, an intersects DC at point n. angle man is 45 degrees. Angle man rotates clockwise around point a, and its two sides intersect CB and DC at point m and N respectively. When angle man rotates around point a to BM = DN, it is easy to prove BM + DN = Mn. When angle man rotates around point a to BM not = DN, what is the relationship between them?

Extend CB to n ', make n'b = nd, connect an' easy to prove, RT △ ABN '≌ RT △ adn ≌ an' = an, ∠ n'ab = ∠ nad ≌ man '= ∠ mAb + ∠ n'ab = ∠ mAb + ∠ nad = ∠ bad - ∠ man = 90 ° - 45 ° = 45 ° = ∠ man, am = am ≌ man' ≌ man (SAS) ≠ Mn '= Mn ≌ BM + DN = BM + BN' = Mn '= Mn