Question

kiran is using the diagram to prove the statement, \if a parallelogram has one right angle, it is a rectangle.\ given that efgh is a parallelogram and angle hef is right, which reasoning about angles will help him prove that angle fgh is also a right angle?
corresponding angles are congruent when parallel lines are cut by a transversal.
opposite angles in a parallelogram are congruent.
vertical angles are congruent.
the base angles of an isosceles triangles are congruent.

Explanation:

Step1: Recall properties of parallelograms

In a parallelogram, opposite angles are congruent.

Step2: Analyze the given parallelogram \(EFGH\)

Given that \(\angle HEF\) is a right angle (\(90^{\circ}\)).
Since \(EFGH\) is a parallelogram, \(\angle FGH\) and \(\angle HEF\) are opposite angles.
By the property of parallelograms (opposite angles are congruent), \(\angle FGH=\angle HEF\).

Answer:

Opposite angles in a parallelogram are congruent.