MNO and

Question

PQR are known to have two pairs of congruent corresponding angles. Which of these statements must be true?



I. There are at least two pairs of congruent corresponding sides.



II.
MNO and
PQR are dilations of each other.



III. The triangles are similar.

MNO and
PQR are known to have two pairs of congruent corresponding angles. Which of these statements must be true?



I. There are at least two pairs of congruent corresponding sides.



II.
MNO and
PQR are dilations of each other.



III. The triangles are similar.

II only

II and III

I, II, and III

III only

Answer 1

The correct statement is: III only

If two triangles have two pairs of congruent corresponding angles, then by the AA (angle-angle) similarity criterion, the triangles are similar. This means that the corresponding sides are proportional, but not necessarily congruent. So statement I (there are at least two pairs of congruent corresponding sides) is not necessarily true. Statement II (MNO and PQR are dilations of each other) does not necessarily follow from the given information about congruent corresponding angles.