Similar Triangles

Two angles are equal (AA similarity), All three sides are proportional (SSS similarity), Two sides are proportional and included angle is equal (SAS similarity), All three angles are equal (AAA similarity)

The similarity criteria are: AA (two angles equal), SSS (all sides proportional), SAS (two sides proportional with included angle equal), and AAA (all angles equal, which is equivalent to AA). Having just one side and one angle equal is insufficient for similarity.

12 cm

Since triangles are similar, corresponding sides are proportional. AB/PQ = BC/QR, so 6/9 = 8/QR. Cross multiplying: 6 × QR = 8 × 9, so 6 × QR = 72, therefore QR = 12 cm.

True

All congruent triangles are similar because they have the same shape and size. If triangles are congruent, their corresponding angles are equal and corresponding sides are in the ratio 1:1, which satisfies the conditions for similarity.

8 cm

By the Basic Proportionality Theorem, AD/DB = AE/EC. Substituting: 3/6 = 4/EC. Cross multiplying: 3 × EC = 6 × 4, so 3 × EC = 24, therefore EC = 8 cm.