Question 1: D and E are points on the sides AB and AC respectively of a ∆ABC such that DE || BC. (i) If AD = 3.6 cm, AB = 10 cm and AE = 4.5 cm, find EC and AC. (ii) If AB = 13.3 cm, AC = 11.9 cm and EC = 5.1 cm, find AD. (iii) If AD/DB = 4/7 and AC = 6.6 cm, find AE. (iv) if AD/AB = 8/15 and EC = 3.5 cm, find AE.
D and E are points on the sides AB and AC respectively of an ∆ABC such that DE || BC. Find the value of x, when (i) AD = x cm, DB = (x – 2) cm, AE = (x + 2) cm and EC = (x – 1) cm. (ii) AD = 4 cm, DB = (x – 4) cm, AE = 8 cm and EC = (3x – 19) cm. (iii) AD = (7x – 4) cm, AE = (5x – 2) cm, DB = (3x + 4) and EC = 3x cm.
D and E are points on the sides AB and AC respectively of a ∆ABC. In each of the following cases, determine whether DE || BC or not. (i) AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm (ii) AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm. (iii) AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm. (iv) AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.
In a ∆ABC, AD is the bisector of ∠A. (i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC. (ii) If AB = 10 cm, AC = 14 cm and BC – 6 cm, find BD and DC. (iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC. (iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.
M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that (i) DM/MN = DC/BN (ii) DN/DM = AN/DC
Show that the line segment which joins the midpoints of the oblique sides of a the trapezium is parallel to the parallel sides.
In each of the given pairs of triangles, find which pair of triangles are similar. State the
similarity criterion and write the similarity relation in symbolic form:
In the given figure, if ∠ADE = ∠B, show that ΔADE ~ ΔABC. If AD = 3.8 cm, AE = 3.6 cm, BE
= 2.1 cm and BC = 4.2 cm, find DE.
2: The areas of two similar triangles ABC and PQR are in the ratio 9: 16. If BC = 4.5 cm, find
the length of QR.
The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find
the ratio of their areas.
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