Question

what triangle congruence theorem could you use to prove that triangle ade is congruent to triangle cbe? justify your choice. 1. sss (side - side - side) all three corresponding sides are equal in length. 2. sas (side - angle - side) a pair of corresponding sides and the included angle (the angle formed when the two lines meet) are equal. 3. asa (angle - side - angle) a pair of corresponding angles and the included side are equal.

Explanation:

From the figure, we can see that there are pairs of equal - length sides and equal angles. The vertical angles at E are equal. If we can identify a pair of corresponding sides and the included angle that are equal between \(\triangle ADE\) and \(\triangle CBE\), we can use the SAS (Side - Angle - Side) congruence theorem. For example, if we know that \(AE = CE\), \(\angle AED=\angle CEB\) (vertical angles) and \(DE = BE\), then by the SAS theorem, \(\triangle ADE\cong\triangle CBE\).

Answer:

SAS (Side - Angle - Side)