Question

select all statements that must be true. a the sum of the angles of a parallelogram is 360°. b the opposite angles in a parallelogram are congruent. c a kite is a parallelogram. d the diagonals of a parallelogram bisect the angles. e opposite sides of a parallelogram are congruent.

Explanation:

Step1: Recall polygon - angle sum formula

The sum of interior angles of an \(n\) - sided polygon is \((n - 2)\times180^{\circ}\). For a parallelogram (\(n=4\)), \((4 - 2)\times180^{\circ}=360^{\circ}\), so statement A is true.

Step2: Recall parallelogram properties

In a parallelogram, opposite angles are congruent. This is a fundamental property of parallelograms, so statement B is true.

Step3: Analyze the definition of a kite and parallelogram

A kite has two pairs of adjacent - equal sides, while a parallelogram has two pairs of opposite - equal sides. A kite is not a parallelogram, so statement C is false.

Step4: Recall the property of parallelogram diagonals

The diagonals of a parallelogram bisect each other, but they do not necessarily bisect the angles (except for special parallelograms like rhombuses). So statement D is false.

Step5: Recall parallelogram side - length property

One of the key properties of a parallelogram is that opposite sides are congruent. So statement E is true.

Answer:

A. The sum of the angles of a parallelogram is \(360^{\circ}\), B. The opposite angles in a parallelogram are congruent, E. Opposite sides of a parallelogram are congruent.