quadrilateral is a parallelogram. if consecutive angles are congruent, which statement(s) must be true
Any choices??
To determine which statement(s) must be true if a quadrilateral is a parallelogram and its consecutive angles are congruent, we can recall some properties of parallelograms:
1. Opposite sides of a parallelogram are parallel.
2. Opposite sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary (add up to 180 degrees).
Based on these properties, we can deduce that the following statement(s) must be true:
1. Opposite sides of the quadrilateral are parallel.
- This is true for all parallelograms. If the given quadrilateral is a parallelogram, then its opposite sides must be parallel.
2. Opposite angles of the quadrilateral are congruent.
- This is also true for all parallelograms. If the given quadrilateral is a parallelogram and its consecutive angles are congruent, then its opposite angles must be congruent.
Please note that the information provided does not guarantee that all four angles of the given quadrilateral are congruent. Only the consecutive angles are specified to be congruent.