Question

In parallelogram ABCD, if 1) They are congruent by SAS

2) They are congruent by ASA
3) They are congruent by SSS
4) They are similar by SAS

Answer 1

In parallelogram ABCD, congruence can be determined using different combinations of sides and angles: SAS, ASA, and SSS. Parallelograms can also be similar by SAS condition.

Step-by-step explanation:

In parallelogram ABCD, congruence can be determined using different combinations of sides and angles:

1. If the corresponding sides and the included angles of the parallelogram are congruent to another parallelogram, then they are congruent by SAS (Side-Angle-Side) condition.
2. If the corresponding angles of the parallelogram are congruent to another parallelogram, then they are congruent by ASA (Angle-Side-Angle) condition.
3. If all four sides of the parallelogram are congruent to another parallelogram, then they are congruent by SSS (Side-Side-Side) condition.

However, two parallelograms can be similar by SAS (Side-Angle-Side) condition.