Ask a math question, it's the third day of junior high school Arbitrarily make a quadrilateral. And connect the midpoint of its four sides in turn. Get a new quadrilateral. This quadrilateral is a parallelogram. How to prove?

Ask a math question, it's the third day of junior high school Arbitrarily make a quadrilateral. And connect the midpoint of its four sides in turn. Get a new quadrilateral. This quadrilateral is a parallelogram. How to prove?

Method 1: a diagonal can be connected, and a group of parallelograms with parallel and equal opposite sides can be obtained by using the knowledge of median line of triangle
Method 2: two diagonals can be connected, and two groups of parallelograms with parallel or equal opposite sides can be obtained by using the knowledge of triangle median line

As shown in the figure, we know that a, B, C and D are four points on ⊙ o, ab = BC, BD intersects AC at point E, connecting CD and ad. (1) prove that DB bisects ∠ ADC; (2) if be = 3, ed = 6, find the length of ab

(1) It is proved that: ∵ AB = BC, ∵ AB = BC, (2 points) ∵ BDC = ∵ ADB, ∵ DB bisection ∵ ADC; (4 points) (2) from (1), we can see that ab = BC, ∵ BAC = ∵ ADB, and ∵ Abe = ∵ abd, ∵ Abe ∵ DBA, (6 points) ∵ Abbe = bdab, ∵ be = 3, ed = 6,