If two angles and any side of a triangle are equal to the corresponding angles and side of another triangle, then prove that the two triangles are congruent.


Answer:


Step by Step Explanation:
  1. Let ABC and DEF be the two triangles with BC=EF,A=D, and B=E.
      A B C D E F
  2. We have to prove that ABCDEF
  3. We know that the sum of the angles of a triangle is 180. A+B+C=D+E+F=180(1) It is given that A=D and B=E.
    Thus, from equation (1), we conclude that C=F.
  4. In ABC and DEF, we have BC=EF[By step 1]C=F[By step 3]B=E[By step 1]ABCDEF[By ASA criterion]
  5. Thus, if two angles and any side of a triangle are equal to the corresponding angles and side of another triangle, the two triangles are congruent.

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