Question

Melissa writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: Melissa's proof for triangles AOB and COD, angle 1 is equal to angle 2, as they are vertical angles. AO = OC and BO = OD because it is given that diagonals bisect each other. The triangles AOB and COD are congruent by SAS postulate. Similarly, triangles AOD and COB are congruent. By CPCTC, AB is equal to DC. By CPCTC, AD is equal to BC. As the opposite sides are congruent, the quadrilateral ABCD is a parallelogram. Which is the missing phrase in Melissa's proof?

1) Angles AOB and COD are congruent by ASA postulate
2) Angles AOB and COD are congruent by AAS postulate
3) Angles AOB and COD are congruent by SSS postulate
4) Angles AOB and COD are congruent by SAS postulate

Answer 1

Melissa's missing phrase in her proof should be 'Angles AOB and COD are congruent by SAS postulate.'

Step-by-step explanation:

In Melissa's proof, the missing phrase should be "Angles AOB and COD are congruent by SAS postulate."

To prove that the quadrilateral ABCD is a parallelogram, Melissa shows that the triangles AOB and COD are congruent using the SAS (Side-Angle-Side) postulate.

This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.