Question

given the figures markings and ( mangle a = 55^{circ} ) and ( mangle b = 125^{circ} ) which theorem can be used to prove that the quadrilateral is a parallelogram?

theorem 33
theorem 34
theorem 35
theorem 36
not a parallelogram

Explanation:

Step1: Recall the theorem of parallelogram

The theorem of parallelogram: If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.

Step2: Analyze the given information

In the figure, one pair of opposite sides are marked as congruent. Also, \(m\angle A = 55^{\circ}\) and \(m\angle B=125^{\circ}\), and \(m\angle A + m\angle B=55^{\circ}+ 125^{\circ}=180^{\circ}\). So, the two sides are parallel (because consecutive interior angles are supplementary).

Step3: Apply the theorem

Since one pair of opposite sides are both parallel and congruent, we can use the theorem that if one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram. (Assuming this is Theorem 34 in the relevant textbook's numbering system)

Answer:

Theorem 34