Question

1. which is not a pair of congruent angles in the diagram below? diagram of parallelogram abcd with side/angle markings options: angles abd and bdc; angles bcd and bad; angles bda and dbc; angles abd and bad

Explanation:

Step1: Analyze the parallelogram properties

The figure is a parallelogram (since opposite sides are marked equal). In a parallelogram, opposite angles are congruent, alternate - interior angles (formed by a transversal) are congruent.

• For angles \(ABD\) and \(BDC\): \(AB\parallel CD\) and \(BD\) is a transversal. By the alternate - interior angles theorem, \(\angle ABD\cong\angle BDC\).
• For angles \(BCD\) and \(BAD\): In a parallelogram, opposite angles are congruent. So \(\angle BCD\cong\angle BAD\).
• For angles \(BDA\) and \(DBC\): \(AD\parallel BC\) and \(BD\) is a transversal. By the alternate - interior angles theorem, \(\angle BDA\cong\angle DBC\).
• For angles \(ABD\) and \(BAD\): There is no property (like alternate - interior angles, opposite angles of parallelogram) that guarantees these two angles are congruent. In a parallelogram, \(AB = AD\) is not given (the markings show \(AB = CD\) and \(AD=BC\), but not \(AB = AD\)), so \(\triangle ABD\) is not isosceles, so \(\angle ABD\) and \(\angle BAD\) are not necessarily congruent.

Answer:

angles ABD and BAD