Question

look at the quadrilateral shown below: clara writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: claras proof 1. for triangles aob and cod, angle 1 is equal to angle 2, as they are vertical angles. 2. ao = oc and bo = od because it is given that diagonals bisect each other. 3. the triangles aob and cod are congruent by sas postulate. 4. similarly, triangles aod and cob are congruent. 5. by _, angle abd is equal to angle cdb and angle adb is equal to angle cbd. 6. as the alternate interior angles are congruent, the opposite sides of quadrilateral abcd are parallel. 7. therefore, abcd is a parallelogram. which is the missing phrase in claras proof? cpctc property of parallelograms transitive property vertical angles theorem

Explanation:

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used to show that corresponding angles of congruent triangles are equal. Since triangles AOB and COD are congruent, and triangles AOD and COB are congruent, to get that angle ABD is equal to angle CDB and angle ADB is equal to angle CBD, we use CPCTC.

Answer:

CPCTC