GSEB Class 7 Maths Solutions Chapter 10 Practical Geometry Exercise 10.2

Question 1. Construct \( \triangle XYZ \) in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.
Answer:

Steps of construction:

1. Draw a line segment YZ = 5 cm.
2. With center Y and radius 4.5 cm, draw an arc.
3. With center Z and radius 6 cm, draw another arc to cut the previous arc at X.
4. Join YX and ZX.

Thus, \( \triangle XYZ \) is the required triangle.

Exam Tip: Remember to use a compass and ruler accurately for precise construction. Always draw the base first and then use arcs from its endpoints to locate the third vertex.

Question 2. Construct an equilateral triangle of side 5.5 cm.
Answer:

Steps of construction:

1. Draw a line segment BC = 5.5 cm.
2. With B as the center and a radius of 5.5 cm, draw an arc.
3. With C as the center and a radius of 5.5 cm, draw another arc to cut the previous arc at A.
4. Join BA and CA.

Thus, \( \triangle ABC \) is the required equilateral triangle.

Exam Tip: For an equilateral triangle, all three sides are of equal length. Make sure your compass settings are consistent for all arcs.

Question 3. Draw \( \triangle PQR \) with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?
Answer:

Steps of construction:

1. Draw a line segment QR = 3.5 cm.
2. With Q as the center and a radius of 4 cm, draw an arc.
3. With R as the center and a radius of 4 cm, draw another arc such that it cuts the previous arc at P.
4. Join QP and RP.

Thus, \( \triangle PQR \) is the required triangle. Since PQ = PR = 4 cm, \( \triangle PQR \) is an isosceles triangle.

Exam Tip: Remember that a triangle with two sides of equal length is an isosceles triangle. Clearly state the type of triangle after completing its construction.

Question 4. Construct \( \triangle ABC \) such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure \( \angle B \).
Answer:

Steps of construction:

1. Draw a line segment BC = 6 cm.
2. With B as the center and a radius of 2.5 cm, draw an arc.
3. With C as the center and a radius of 6.5 cm, draw another arc such that it cuts the previous arc at A.
4. Join BA and CA.

Thus, \( \triangle ABC \) is the required triangle. On measuring, we find that \( \angle B = 90^\circ \).

Exam Tip: After constructing the triangle, always verify the angle measurement using a protractor. Recognizing Pythagorean triples \( (2.5, 6, 6.5) \) can sometimes indicate a right-angled triangle.