Question

Given:

BD and AD intersect at point C
BC is congruent to BC
AC is congruent to DC
AB and DE are drawn
Which of the following is the correct way to prove triangle ABC is congruent to triangle DEC?
Hypotenuse, Leg
Angle, Side, Angle
Side, Angle, Side
Side, Side, Side

Answer 1

To prove triangle ABC is congruent to triangle DEC, we can use the Angle-Side-Angle (ASA) congruence criterion.

Step-by-step explanation:

To prove triangle ABC is congruent to triangle DEC, we can use the Angle-Side-Angle (ASA) congruence criterion. According to the given information, we have the following congruent parts: CBC is congruent to DCAB, BC is congruent to AC, and DE is drawn.

1. Angle: Angle BCD is congruent to Angle ACD (by the Angle-Angle criterion).

2. Side: Segment BC is congruent to Segment AC (given).

3. Angle: Angle BAC is congruent to Angle DCE (by the Angle-Angle criterion).

Therefore, by the ASA criterion, we can conclude that triangle ABC is congruent to triangle DEC.