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:
- Let △ABC and △DEF be the two triangles with BC=EF,∠A=∠D, and ∠B=∠E.
- We have to prove that △ABC≅△DEF
- 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. - In △ABC and △DEF, we have BC=EF[By step 1]∠C=∠F[By step 3]∠B=∠E[By step 1]∴△ABC≅△DEF[By ASA criterion]
- 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.