180k views
4 votes
Given BD and AC bisects each other. prove AB\\ CD

Given BD and AC bisects each other. prove AB\\ CD-example-1

1 Answer

4 votes

From step #6, AB is congruent to CD by CPCTC or Corresponding Parts of Congruent Triangles are Congruent.

Triangles ABE and CDE are congruent by SAS postulate.

Therefore, angle B and angle D are congruent.

Note that the segment BD is a transversal line that cuts AB and CD, and angle B and angle D are alternate interior angles.

The answer is :

XY || WZ ⇒ AB || CD

with a reason of :

Parallel lines cut by a transversal form congruent alternate interior angles.

User ZephDavies
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.