ICSE Class 10: Basic Proportionality Theorem Videos | Derivation of BP theorem

KP = 1.4 and KM = 5.6

⇒ PM = KM − KP = 5.6 − 1.4 = 4.2 cm

Again, KQ = 1.8 and KN = 7.2

⇒ QN = KN − KQ = 7.2 − 1.8 = 5.4 cm

KP/PM = 1/3 KQ/QN = 1/3 KP/PM = KQ/QN PQ is parallel to MN. 

By the basic proportionality theorem,

AD/DB = AE/EC 3/5 = AE/(5.6 − AE) AE = 2.1 

Two triangles are congruent if they have corresponding sides equal and corresponding angles equal.

If two triangles have corresponding angles equal, then the triangles are similar.