Let's say you have two line segments, AB and CD which bisect each other at point E. Explain why AC = DB.

When segments AB and CD bisect each other at point E, the two triangles formed, , are congruent to each other SAS Congruence Theorem, therefore, AC = DB.

Recall:

Line segments AB bisecting line segment CD at point E will give us the triangles AEC and BED if we join A to C, and B to D.

Thus, the following information can be deduced from the image of both triangles shown in the attachment below:

(congruent segments)

(vertical angles)

From the above stated, by the SAS Congruence Theorem.

Since both triangles are congruent, all their corresponding sides would be congruent, therefore AC = DB.

In summary, when segments AB and CD bisect each other at point E, the two triangles formed, , are congruent to each other SAS Congruence Theorem, therefore, AC = DB.

Learn more here:

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(corresponding parts of congruent triangles are equal)

Step-by-step explanation:

Consider triangles ACE and BDE.

As AB and CD bisect each other at point E,

As AB and CD intersect each other at point E and vertically opposite angles are equal,

∠AEC = ∠BED

So,

ΔAEC ≅ ΔBED       (Using SAS congruence criteria)

(According to SAS congruence criteria, if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle then the two triangles are said to be congruent.)

Hence,

(corresponding parts of congruent triangles are equal)

answer:

a=9

step-by-step explanation: lmk if you need a explanation