Question

definition of ≅ △s
side - side - side (sss)
side - angle - side sas
angle - angle - side (aas)
angle - side - angle (asa)
hypotenuse - leg (hl)

Explanation:

Step1: Analyze the given information

We have two triangles. One pair of sides is marked as equal (the sides with the double - hash marks). One pair of angles (\(80^{\circ}\)) is equal. But we don't know if the included angles (the angles between the known side and the other sides) are equal.

Step2: Recall the congruence criteria

• SSS: Requires three pairs of equal sides. We don't have information about three pairs of sides.
• SAS: Requires two pairs of sides and the included angle to be equal. We don't know if the included angles are equal.
• AAS: Requires two pairs of angles and a non - included side to be equal. We only have one pair of known angles (\(80^{\circ}\)).
• ASA: Requires two pairs of angles and the included side to be equal. We only have one pair of known angles (\(80^{\circ}\)).
• HL: Is for right - angled triangles. There is no indication that these are right - angled triangles.
• Definition of \(\cong\triangle s\): Just a general statement, not a criterion for proving congruence from given information.

Since we have no valid congruence criterion (SSS, SAS, AAS, ASA, HL) satisfied with the given information (only one pair of sides and one pair of non - included angles), we cannot prove the triangles congruent.

Answer:

We cannot prove the triangles congruent as there is not enough information to satisfy any of the congruence criteria (SSS, SAS, AAS, ASA, HL).