4. Given parallelogram WXYZ , determine weather each statement below is true or false

Question

∠X and ∠Y are opposite, congruent angles.
∠X and ∠Z are opposite, congruent angles.
WX¯¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides.
WZ¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides

Answer 1

First, let's understand the properties of a parallelogram. In a parallelogram:
- Opposite angles are congruent.
- Opposite sides are congruent.

Using these properties, we can determine the truth or falsity of the given statements:

1. ∠X and ∠Y are opposite, congruent angles.
- True. Since X and Y are opposite angles in a parallelogram, they are congruent.

2. ∠X and ∠Z are opposite, congruent angles.
- False. In a parallelogram, ∠X and ∠Z are not opposite angles. Instead, they are adjacent angles.

3. WX¯¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides.
- False. In a parallelogram, WX¯¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are not opposite sides.

4. WZ¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides.
- True. In a parallelogram, WZ¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite sides and they are also congruent.