Given ABCE is a rectangle, D is the midpoint of CE

Question

Prove AD =~ BD

Answer 1

To prove that AD is congruent to BD, we can use the definition of a midpoint.

Definition of a midpoint: A midpoint is a point that divides a line segment into two congruent segments.

In this case, D is the midpoint of CE, which means that CD is congruent to DE.

Now, let's consider the triangle ACD and the triangle BCD.

AC is congruent to BC because they are opposite sides of the rectangle.

CD is congruent to CD by the reflexive property of congruence.

Therefore, we have ASA congruence, where angle ACD is congruent to angle BCD, side AC is congruent to side BC, and side CD is congruent to side CD.

By the ASA congruence theorem, triangle ACD is congruent to triangle BCD.

Therefore, AD is congruent to BD by the corresponding parts of congruent triangles are congruent (CPCTC) theorem.