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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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FAQs on Textbook Solutions: Geometric Constructions - Mathematics Class 10 (Maharashtra SSC Board)

1. What are geometric constructions and why are they important in geometry?
Ans. Geometric constructions are methods of drawing shapes, angles, and lines using only a compass and a straightedge. They are important in geometry because they help in understanding fundamental concepts, proving theorems, and developing spatial reasoning skills. By practicing these constructions, students enhance their problem-solving abilities and gain a deeper appreciation for geometric relationships.
2. What tools are typically used in geometric constructions?
Ans. The primary tools used in geometric constructions are a compass and a straightedge (ruler without markings). The compass is used to draw arcs and circles, while the straightedge is used to draw straight lines. These tools allow for precise and accurate constructions following the rules of classical geometry.
3. How can one construct a perpendicular bisector of a given line segment?
Ans. To construct a perpendicular bisector of a given line segment, follow these steps: 1. Place the compass point on one endpoint of the segment and draw an arc above and below the line. 2. Without changing the compass width, repeat from the other endpoint to create two intersecting arcs. 3. Draw a straight line through the points where the arcs intersect. This line is the perpendicular bisector, which divides the segment into two equal parts at a right angle.
4. What is the significance of geometric constructions in real-life applications?
Ans. Geometric constructions have significant real-life applications, especially in fields such as architecture, engineering, and design. They aid in creating accurate blueprints and models, ensuring structures are built with precision. Additionally, these constructions are fundamental in fields involving spatial analysis and navigation, making them essential for various practical tasks.
5. Can geometric constructions be performed using software?
Ans. Yes, geometric constructions can be performed using various software applications designed for geometry, such as GeoGebra and Cabri Geometry. These tools provide a digital environment for creating and manipulating geometric figures, allowing users to explore properties and relationships interactively. While software can enhance understanding, practicing constructions by hand is essential for mastering the concepts.
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