Justify the last two steps of the proof.
Given: ABCD is a parallelogram.
Prove: ΔABC is congruent to ΔCDA
The figure shows parallelogram A B C D with diagonal A C.
ABDC is a parallelogram.
AB is congruent to DC and BC is congruent to DA
AC is congruent to CA
ΔABC is congruent to ΔCDA
Given
Opposite sides of a parallelogram are congruent.
_____________________?
_____________________?
The last two steps of the proof can be justified as follows:
1. Opposite sides of a parallelogram are congruent: This is a known property of parallelograms. In a parallelogram, the opposite sides are parallel and congruent.
2. AC is congruent to CA: This is the reflexive property of congruence. Any segment or line is congruent to itself.
Therefore, ΔABC is congruent to ΔCDA.