Page 1
Geometric Constructions
Practice Set 4.1
Q. 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 ?ABC is similar to ?LMN
? corresponding sides will have same ratio
Now, as
? LM = 4.4 cm
? MN = 4.8 cm
Page 2
Geometric Constructions
Practice Set 4.1
Q. 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 ?ABC is similar to ?LMN
? corresponding sides will have same ratio
Now, as
? LM = 4.4 cm
? MN = 4.8 cm
? LN = 3.6 cm
Now, make a ?LMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm
Q. 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.
Page 3
Geometric Constructions
Practice Set 4.1
Q. 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 ?ABC is similar to ?LMN
? corresponding sides will have same ratio
Now, as
? LM = 4.4 cm
? MN = 4.8 cm
? LN = 3.6 cm
Now, make a ?LMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm
Q. 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
Page 4
Geometric Constructions
Practice Set 4.1
Q. 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 ?ABC is similar to ?LMN
? corresponding sides will have same ratio
Now, as
? LM = 4.4 cm
? MN = 4.8 cm
? LN = 3.6 cm
Now, make a ?LMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm
Q. 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.
Q. 3. ? RST ~ ? XYZ. In ? RST, RS = 4.5 cm, ?RST = 40°, ST = 5.7 cm.
Construct ?RST and ?XYZ, such that
Page 5
Geometric Constructions
Practice Set 4.1
Q. 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 ?ABC is similar to ?LMN
? corresponding sides will have same ratio
Now, as
? LM = 4.4 cm
? MN = 4.8 cm
? LN = 3.6 cm
Now, make a ?LMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm
Q. 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.
Q. 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 ?RST is similar to ?XYZ,
? 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.
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