It is known that: as shown in the figure, in △ ABC, ∠ C = 90 °, cm ⊥ AB in M, at bisection ∠ BAC intersects cm in D, intersects BC in T, de ∥ AB through D intersects BC in E, verification: CT = be

It is known that: as shown in the figure, in △ ABC, ∠ C = 90 °, cm ⊥ AB in M, at bisection ∠ BAC intersects cm in D, intersects BC in T, de ∥ AB through D intersects BC in E, verification: CT = be

It is proved that: TF ⊥ AB is made in F through t, ∵ at bisection ⊥ BAC, ∵ ACB = 90 °, CT = TF (the distance from the point on the bisection line to both sides of the angle is equal), ∵ ACB = 90 °, cm ⊥ AB, ∵ ADM + ⊥ dam = 90 °, ATC + ⊥ cat = 90 °, ∵ at bisection ⊥ BAC, ∵ dam = ⊥ cat, ∵ ADM = ⊥ ATC