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Answer :
Final answer:
The given statement ajlk = alnm can be proved using the corresponding angles theorem and the fact that l is the midpoint of jn. By applying these properties and using the transitive property of equality, we can conclude that the triangles ∆ajk and ∆alm are congruent, which implies that ajlk = alnm.
Explanation:
To prove that ajlk = alnm, we can use the corresponding angles theorem and the fact that l is the midpoint of jn.
Given: jk || lm, jk = lm, l is the midpoint of jn
Statement 1: jk || lm (Given)
Statement 2: jk = lm (Given)
Statement 3: l is the midpoint of jn (Given)
Statement 4: ∠ajk = ∠alm (Corresponding angles theorem)
Statement 5: ∠jkl = ∠lkm (Corresponding angles theorem)
Statement 6: ∠ajk = ∠jkl (Vertical angles are congruent)
Statement 7: ∠alm = ∠lkm (Vertical angles are congruent)
Statement 8: ∠ajk = ∠jkl = ∠alm = ∠lkm (Transitive property of equality)
Statement 9: ∆ajk ≅ ∆alm (Angle-side-angle congruence)
Statement 10: ajlk = alnm (Corresponding parts of congruent triangles are congruent)
Therefore, we have proved that ajlk = alnm using the given information and the corresponding angles theorem.
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