a If the triangles are congruent, they must also be similar. This means they have at least two pairs of congruent angles. In each triangle, we know the measure of two angles. With this information we can determine the measure of the unknown angle in each triangle.
62^(∘)+48^(∘) +m∠ C&=180^(∘) ⇔ m∠ C=70^(∘)
62^(∘)+70^(∘) +m∠ D&=180^(∘) ⇔ m∠ D=48^(∘)
The triangles have three pairs of congruent angles. This means they are, in fact, similar. If the triangles are also congruent, they should in addition to this have three pairs of congruent sides. From the diagram we can identify two corresponding sides.
Since AC and EF do not have the same length, the triangles cannot be congruent.
Also, ∠ ACB and ∠ DCB form a linear pair, which means they are supplementary angles. Since one of these angles is a right angle, the second one has to be a right angle as well.
c Examining the diagram, we notice that none of the angles are known. Therefore, the only way we can claim congruence is if the triangles have three pairs of congruent sides. Examining the diagram, we see that this is the case.
