Emil says that if two pairs of corresponding angles of two triangles are congruent, then this is enough information to prove that the two triangles are similar. Is he correct?
Yes, because if you draw triangles that have two pairs of congruent angles, the triangles always appear to have the same shape.
No, because lengths are not given, so you cannot tell if the side lengths are in proportion.
No, because ΔDOG must be rotated before it can be dilated to match ΔCAT exactly.
Yes, because it can be shown that ΔDOG can be rotated and then dilated to match ΔCAT exactly.
Yes, because it can be shown that ΔDOG can be rotated and then dilated to match ΔCAT exactly.
This statement is correct because when two pairs of corresponding angles in two triangles are congruent, the third pair of angles must also be congruent due to the triangle sum property (the angles in a triangle add up to 180 degrees). Therefore, the two triangles are similar by the Angle-Angle (AA) similarity postulate, which indicates that corresponding sides will be in proportion, even if the lengths are not provided explicitly.