E And C are mid points od line AD and line DB; line AD is congruent to line DB and angle A is congruent to angle 1. What do you do to prove that ABCE is a isosceles trapezod ??

Check your previous posting.

To prove that ABCE is an isosceles trapezoid, we need to show that the opposite sides are congruent and that one pair of opposite angles are congruent.

Here's how we can prove it:

Step 1: Given information:
- Line AD and line DB are congruent.
- Angle A is congruent to angle 1.
- E and C are the midpoints of line AD and line DB, respectively.

Step 2: Establishing congruent sides:
Since E and C are midpoints of AD and DB, respectively, we know that EC is parallel to AB (by the midpoint theorem) and that EC is equal to 1/2 of AB (by the definition of midpoint). Therefore, EC = 1/2 AB.

Step 3: Establishing congruent angles:
Angle A is congruent to angle 1, and AB is parallel to EC. By the Alternate Interior Angle Theorem (or Corresponding Angles Theorem), we know that the alternate interior angles are congruent. Therefore, angle B is congruent to angle C.

Step 4: Proving equal opposite sides:
Now, we have EC = 1/2 AB and angle B congruent to angle C. To prove the other set of opposite sides are congruent, we can use the properties of a trapezoid. In a trapezoid, the non-parallel sides are congruent if and only if the base angles are congruent. Since angle A is congruent to angle 1, and angle B is congruent to angle C, we can conclude that side AB is congruent to side EC.

Step 5: Conclusion:
We have shown that opposite sides AB and EC are congruent and that one pair of opposite angles (∠B and ∠C) are congruent. Therefore, ABCE is an isosceles trapezoid.

In summary, to prove that ABCE is an isosceles trapezoid, we established that EC is parallel to AB, EC is equal to 1/2 AB, angle B is congruent to angle C, and AB is congruent to EC.