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 ??
To prove that ABCD is an isosceles trapezoid, you need to establish that one pair of opposite sides are parallel and another pair of opposite sides are congruent.
Here is a step-by-step explanation of how to prove that ABCD is an isosceles trapezoid:
1. Given that E and C are the midpoints of line AD and line DB, respectively, we can conclude that AE is congruent to EC and CD is congruent to DB. This is because E and C being midpoints implies that they divide the sides AD and DB into equal halves.
2. Given that AD is congruent to DB, we have another pair of congruent sides.
3. Using the Transitive Property of Congruence, we can state that AE is congruent to EC is congruent to CD.
4. Now, let's consider the angles. Given that angle A is congruent to angle 1, we can conclude that angle ABC is also congruent to angle 1. This is due to the fact that the angles in a straight line always add up to 180 degrees, and angle A and angle ABC form a straight line.
5. Since angle ABC is congruent to angle 1 and AE is congruent to EC, we can use the Converse of the Alternate Interior Angles Theorem to establish that line AB is parallel to line CD.
6. Lastly, combining the fact that AB is parallel to CD with the congruent sides AE and CD, we can conclude that ABCD is an isosceles trapezoid. By definition, a trapezoid is isosceles if it has one pair of opposite sides that are parallel and another pair of opposite sides that are congruent.
Therefore, you can prove that ABCE is an isosceles trapezoid by showing that one pair of opposite sides (AB and CD) are parallel and another pair of opposite sides (AE and CD) are congruent, while also considering the congruent angles (angle A and angle 1).