Answer :

The ∆ABX and ∆CDX formed after the mutual bisection of AC and BD each other at point X are congruent i.e ΔABX ≅ ΔCDX, by SAS congruance theorem.

SAS congruence theorem: "SAS " stands for "Side-Angle-Side". If there is two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are said to be congruent. We have , A Quadrilateral ABCD, such that AC and BD bisect each other at point X. After bisection there is formed 4 triangles. We have to show ΔABX ≅ ΔCDX by SAS Congruance Rule. Now, as we know that bisect point divides the sides into two equal parts, i.e, AX = CX and DX = BX. So, in ΔABX and ΔCDX

  • AX = CX ( since X is bisecter point )
  • BX = DX ( from bisection )
  • m∠AXB = m∠CXD ( corresponding angles)

As we see ∠AXB is angle in between to two sied AX and BX . Similarly, ∠CXD is in between CX and DX . So, by using SAS congruance theorem ∆ABX is congruent to ∆CDX i.e., ΔABX ≅ ΔCDX.

To learn more about SAS Congruance threoem, refer:

https://brainly.com/question/18922904

#SPJ4

Thanks for taking the time to read Given that AC and BD bisect each other prove that ΔABX ΔCDX using the SAS congruence theorem. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada