a If the triangles are similar they have at least two pairs of congruent angles. In each triangle we know the measure of two angles. By the Triangle Angle Sum Theorem, we can determine the measure of the unknown angle in each triangle.
56^(∘)+34^(∘) +m∠ A&=180^(∘) ⇔ m∠ A=90^(∘)
90^(∘)+34^(∘) +m∠ K&=180^(∘) ⇔ m∠ K=34^(∘)
The triangles have at least two pairs of congruent angles, which means they are similar by the AA (Angle-Angle) Similarity Theorem.
△ ABC ~ △ LKH
b In similar triangles the ratio of corresponding sides is identical. If we divide the triangle's longer sides, we notice that this ratio is the same as the ratio of the smaller sides.
6/9 ? = 4/6 ⇔ 2/3 = 2/3
However, this is not enough information to claim congruence. We must also know that the ratio of the third pair of sides is the same as well
