As shown in the figure, in the isosceles triangle ABC, ab = AC, ah is perpendicular to BC, and point E is the point above ah. Extend ah to point F, so that FH = EH. (1) prove that the quadrilateral ebfc is a diamond; (2) if ∠ BAC = ∠ ECF, prove that AC ⊥ CF

As shown in the figure, in the isosceles triangle ABC, ab = AC, ah is perpendicular to BC, and point E is the point above ah. Extend ah to point F, so that FH = EH. (1) prove that the quadrilateral ebfc is a diamond; (2) if ∠ BAC = ∠ ECF, prove that AC ⊥ CF

It is proved that: (1) AB = AC, ah ⊥ CB, BH = HC. (2 points) ∵ FH = eh, the ∵ quadrilateral ebfc is a parallelogram. (2 points) ah ⊥ CB, the ∵ quadrilateral ebfc is a diamond. (2 points) (2 points) it is proved that: ∵ quadrilateral ebfc is a diamond. (2 points) ∵ AB = AC, ah ⊥ CB