###
Similarity Extra HOTS for Practice with solution

In ∆ PQR, AB || QR. If AB is 3 cm, PB is 2 cm and PR is 6 cm, then find the length of of QR.
D is the midpoint of the side BC of ∆ ABC. If P and Q are points on AB and on AC such that DP bisects ∠BDA and DQ bisects ∠ADC, then prove that PQ || BC.
In ∆ ABC, AE is the external bisector of ∠A, meeting BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find CE.
In ∆ ABC, the internal bisector AD of ∠ A meets the side BC at D. If BD = 2.5cm, AB = 5 cm and AC = 4.2 cm, then find DC.
In triangle ABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE || AC and FE || AB.
In triangle PQR, given that S is a point on PQ such that ST is parallel to QR and PA:SQ = 3:5, If PR = 5.6 cm, then find PT.
In Triangle ABC. DE is parallal to BC and AD:DB = 2:3, IF AE = 3.7 cm, Find EC.