.2 points

⑵ Conjecture: The conclusion in (1) has not changed.

Proof: as shown in the figure, extend the intersection and link.

Is the midpoint of the line segment,

.

From the meaning of the question, we can know.

.

,

.

, .

The quadrilateral is a diamond,

, .

By, and the diagonal of the diamond and the edge of the diamond are just on the same straight line.

Available.

.

The quadrilateral is a diamond,

.

.

.

, .

.

Namely.

, ,

, .

.6 points

(3) .8 points

This comment is an exploratory geometric comprehensive problem. The stem of this topic is presented in the form of reading materials, thus reducing the difficulty of the topic. This topic should be improved on the basis of the final exam in Dalian in 2005.

Test sites of this topic: the nature of diamond, congruent triangles, trigonometric function.

Difficulty coefficient: Question 1: 4; Question 2: 3.5; Question 3: 4