Question

If triangle DEC is congruent to triangle BEC,which is true by CPCTC?

Answer 1

Let's go through the possible answer choices one by one

A) BE is congruent to ED
This is true because "BE" and "ED" are formed by the first two letters of BEC and DEC respectively. The triangles are congruent, so the corresponding sides must be congruent. To name a segment, the order does not matter. Writing "DE" is the same as "ED".

B) AC is congruent to BD
False. Point A isn't mentioned at all. We don't know for sure how point A fits in. The statement may be true, or it could easily be false as well. We don't have enough info.

C) Angle BEC = angle DCE
False. The order of the letters is very important. For angle BEC, we have E in the middle so the vertex of the angle is at point E. For angle DCE, the vertex is at point C. If angle BEC = angle DCE, then E and C must correspond; however they don't. Back up at the top, it says "DEC is congruent to BEC", so we see that E corresponds to E, and C corresponds to C. 

D) angle BCA = angle BCD
False. Again we don't know anything about point A. The same issues come up as they did with choice B.

The only true result is choice A