GSEB Class 7 Maths Solutions Chapter 10 પ્રાયોગિક ભૂમિતિ Exercise 10.2

Question 1. Construct triangle XYZ where XY = 4.5 cm, YZ = 5 cm, and ZX = 6 cm.
Answer:

Steps of Construction:
1. Firstly, draw a line segment YZ with a length of 5 cm.
2. Next, with Y as the center, draw an arc with a radius of 4.5 cm.
3. After that, with Z as the center, draw another arc with a radius of 6 cm. This arc should intersect the previous arc at point X.
4. Finally, draw the line segments XY and XZ.
Thus, triangle XYZ is the triangle that was asked for.

Exam Tip: Remember to use a ruler and compass accurately for construction problems. Always label the vertices and side lengths clearly on your diagram.

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

Steps of Construction:
1. Start by drawing a line segment QR with a length of 5.5 cm.
2. Next, with Q as the center, draw an arc using a radius of 5.5 cm.
3. Then, with R as the center, draw another arc of the same radius (5.5 cm). This arc should intersect the first arc at point P.
4. Finally, draw the line segments PQ and PR.
Thus, triangle PQR is the equilateral triangle we needed to construct.

Exam Tip: For equilateral triangles, all three sides are equal, so only one side length needs to be given to construct it.

Question 3. Construct triangle PQR where PQ = 4 cm, QR = 3.5 cm, and PR = 4 cm. What type of triangle is this?
Answer:

Steps of Construction:
1. Begin by drawing a line segment QR with a length of 3.5 cm.
2. Next, with Q as the center, draw an arc using a radius of 4 cm.
3. Then, with R as the center, draw another arc with the same radius of 4 cm. This arc should intersect the previous arc at point P.
4. Finally, draw the line segments PQ and PR.
Thus, triangle PQR is the triangle we were asked to construct.
Now, observing triangle PQR, we notice that PQ = PR = 4 cm.
Therefore, triangle PQR is an isosceles triangle because two of its sides are equal in length.

Exam Tip: Always compare the side lengths after construction to determine the type of triangle (equilateral, isosceles, or scalene).

Question 4. Construct triangle ABC where AB = 2.5 cm, BC = 8 cm, and AC = 6.5 cm. Find the measure of angle B.
Answer:

Steps of Construction:
1. Firstly, draw a line segment BC with a length of 8 cm.
2. Next, with B as the center, draw an arc using a radius of 2.5 cm.
3. After that, with C as the center, draw another arc with a radius of 6.5 cm. This arc should intersect the previous arc at point A.
4. Finally, draw the line segments AB and AC.
Thus, triangle ABC is the triangle that was asked for.
Upon measuring angle B with a protractor, we observe that its measure is 90°.
Therefore, triangle ABC is identified as a right-angled triangle.

Exam Tip: When asked to find an angle, always measure carefully with a protractor after construction. For right-angled triangles, you can also check using the Pythagorean theorem with the side lengths.