Question

question 10
in △abc, m∠a = 35°, ab = 4, and bc = 2. in △def, m∠d = 35°, de = 4, and ef = 2. is △abc ≅ △def? justify your answer.

Explanation:

Step1: Recall triangle congruence criteria

Triangle congruence criteria include SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles). The given information is two sides and a non - included angle.

Step2: Analyze the given information

In \(\triangle ABC\), we have \(AB = 4\), \(BC=2\), and \(m\angle A = 35^{\circ}\). In \(\triangle DEF\), we have \(DE = 4\), \(EF = 2\), and \(m\angle D=35^{\circ}\). The angle is not included between the two sides. For SAS congruence, the angle must be included between the two sides. Since we have SSA (Side - Side - Angle) which is not a valid congruence criterion (except in the case of right - triangles where it is HL).

Answer:

No, \(\triangle ABC\) is not congruent to \(\triangle DEF\). The given information (SSA) does not satisfy any of the triangle congruence criteria (SSS, SAS, ASA, AAS, HL). SSA is not a valid congruence criterion for non - right triangles.