R s aggarwal solutions mathematics class 10 Solutions for Chapter 4 triangles

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 the adjoining figure, ABCD is a trapezium in which CD || AB and its diagonals intersect at O. If AO = (5x – 7) cm, OC = (2x + 1) cm, BO = (7x – 5) cm and OD = (7x + 1) cm, find the value of x.

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.

In the given figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm,

find BC.

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.

ΔABC ~ ΔPQR and ar (ΔABC) = 4ar (ΔPQR). If BC = 12 cm, find QR.

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find

the ratio of their areas.

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q.

If AP = 1 cm, PB = 3cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 1/16 of the area of

ΔABC.

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake

attached to the other end. How far from the base of the pole should the stake be driven so that the

wire will be taut?

Find the length of altitude AD of an isosceles ΔABC in which AB = AC = 2a units and BC =

units.

State the basic proportionality theorem.

State the AA-similarity criterion.

State the SSS-criterion for the similarity of triangles.

If ΔABC ~ ΔDEF such that 2AB = DE and BC = 6 cm, find EF.

In the given figure, DE || BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and

EC = (3x + 19) cm. Find the value of x.