Practice Set 4.1 Geometric Constructions Class 10th Mathematics Part 2 MHB Solution

Practice Set 4.1

1. ∆ ABC ~ ∆ LMN. In ∆ ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ ABC and ∆ LMN…
2. ∆ PQR ~ ∆ LTR. In ∆ PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆ PQR and ∆…
3. ∆ RST ~ ∆ XYZ. In ∆ RST, RS = 4.5 cm, ∠RST = 40°, ST = 5.7 cm. Construct ∆ RST and…
4. ∆ AMT ~ ∆ AHE. In ∆ AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. {am}/{ah} = frac…

Practice Set 4.1

Question 1.

∆ ABC ~ ∆ LMN. In ∆ ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ ABC and ∆ LMN such that 

Answer:

First we draw a triangle ABC, with AB = 5.5 cm, BC = 6 cm and CA = 4.5 cm

Now, as ΔABC is similar to ΔLMN

∴ corresponding sides will have same ratio

Now, as 

⇒ LM = 4.4 cm

⇒ MN = 4.8 cm

⇒ LN = 3.6 cm

Now, make a ΔLMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm

Question 2.

∆ PQR ~ ∆ LTR. In ∆ PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆ PQR and ∆ LTR, such that 

Answer:

Steps of construction:

i. Draw a triangle PQR, with PQ = 4.2 cm, QR = 5.4 cm and PR = 4.8 cm, choosing QR = 5.4 cm as base.

ii. Below QR, draw an acute angle ∠QRX.

iii. Mark four points R1, R2, R3 and R4 on RX, such that RR1 = R1R2 = R2R3 = R3R4. [As ratio is 4:3, we choose 4 points]

iv. Join QR4 and Draw TR3 || QR4

v. Draw LT || PQ.

Question 3.

∆ RST ~ ∆ XYZ. In ∆ RST, RS = 4.5 cm, ∠RST = 40°, ST = 5.7 cm. Construct ∆ RST and ∆XYZ, such that 

Answer:

First we draw a triangle RST, with RS = 4.5 cm, ∠RST = 40° cm and ST = 5.7 cm

Now, as ΔRST is similar to ΔXYZ,

∴ corresponding sides will have same ratio

Now, as 

⇒ XY = 7.5 cm

⇒ YZ = 9.5 cm

Also, Corresponding angles of similar triangles are equal

⇒ ∠RST = ∠XYZ = 40°

Now, draw a triangle XYZ, with XY = 7.5 cm, ∠XYZ = 40° cm and YZ = 9.5 cm.

Question 4.

∆ AMT ~ ∆ AHE. In ∆ AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm.Construct ∆ AHE.

Answer:

Steps of construction:

i. Draw a triangle AMT, with AM = 6.3 cm, ∠TAM = 50° cm and AT = 5.6 cm, choosing AM as base.

ii. Below AM, draw an acute angle ∠MAX.

iii. Mark four points A1, A2, A3, A4, A5, A6 and A7 on AX, such that AA1 = A1A2 =…= A6A7 [As ratio is 7:5, we choose 7 points]

iv. Join MA7 and Draw HA5 || MA7

v. Draw HE || MT