Five key traits of parallelograms: opposites parallel & equal, angles equal & complementary, and diagonals bisecting each other.
The image you sent shows five properties of parallelograms:
The opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Diagonals bisect each other.
Consecutive angles are supplementary (add up to 180 degrees).
These properties can be used to prove other properties of parallelograms or to solve problems involving parallelograms.
The statement "Given: ABCD is a parallelogram. Prove: AAMB ≅ ACMD" can be proven using the properties of parallelograms.
Here is a proof of the statement:
1. ABCD is a parallelogram (given).
2. AB || CD (opposite sides of a parallelogram are parallel).
3. ∠AMB ≅ ∠CMD (opposite angles of a parallelogram are congruent).
4. AM = CM (diagonals of a parallelogram bisect each other).
5. ΔAMB ≅ ΔCMD (AAS congruence).
Therefore, ΔAMB ≅ ΔCMD.