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Which pair of triangles can be proved congruent by the SAS Postulate?

Given: X is the midpoint of both AD and BE

A. ∆ACD and ∆ECB


B. ∆ADE and ∆ABE


C. ∆ABX and ∆EDX

Which pair of triangles can be proved congruent by the SAS Postulate Given X is the midpoint of both AD and BE A ACD and ECB B ADE and ABE C ABX and EDX class=

Respuesta :

This is another one for my "impossible geometry" file.

If X is the midpoint of both AD and BE, then ABDE is a parallelogram, and point C cannot exist.

The congruent segments are
   BX ≅ EX
   AX ≅ DX
Of course, vertical angles AXB and DXE are congruent.
Then, by SAS, the congruent triangles are
   ΔAXB ≅ ΔDXE
or
   ΔABX ≅ ΔDEX

Selection C is close, but has points D and E swapped. The figure is misleading, which may be a contributor to the problem.
Ver imagen sqdancefan

Answer:

A.

Step-by-step explanation:

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