Set 1: Practice Questions for Constructions

Title: Set 1: Practice Questions for Constructions

Question 1:
In a town planning project, the architect needs to construct a road that is perpendicular to another road. Using a compass and ruler, draw a line that is perpendicular to line AB at point C. Explain the steps involved in constructing this line.

Answer 1:
To construct a line perpendicular to line AB at point C, follow these steps:
1. Place the compass point on point C and draw an arc that intersects line AB at two points, D and E.
2. Using the same compass width, place the compass point on point D and draw an arc that intersects the previously drawn arc. Label this point as F.
3. Connect points C and F with a straight line segment. This line is perpendicular to line AB at point C.

Question 2:
A farmer wants to construct a rectangular field with a given length and width. Using a compass and ruler, draw a rectangle with a length of 8 cm and a width of 5 cm. Explain the steps involved in constructing this rectangle.

Answer 2:
To construct a rectangle with a length of 8 cm and a width of 5 cm, follow these steps:
1. Draw a line segment AB of length 8 cm using a ruler. This will represent the length of the rectangle.
2. From point A, draw a perpendicular line segment AC of length 5 cm using a ruler and compass.
3. Using point C as the center, draw arcs with a radius equal to the length of AB (8 cm) on both sides of line segment AC.
4. Label the points where the arcs intersect the line segment AB as D and E.
5. Connect points A, B, D, and E to form a rectangle with a length of 8 cm and a width of 5 cm.

Question 3:
A surveyor needs to construct a triangle with sides measuring 6 cm, 8 cm, and 10 cm. Using a compass and ruler, draw this triangle. Explain the steps involved in constructing this triangle.

Answer 3:
To construct a triangle with sides measuring 6 cm, 8 cm, and 10 cm, follow these steps:
1. Draw a line segment AB of length 8 cm using a ruler. This will be one side of the triangle.
2. From point A, draw a line segment AC of length 6 cm using a ruler and compass.
3. Using point C as the center, draw an arc with a radius equal to the length of AB (8 cm).
4. Using point A as the center, draw an arc with a radius equal to the length of AC (6 cm).
5. The intersection point of the two arcs is point D.
6. Connect points A, B, and D to form the triangle with sides measuring 6 cm, 8 cm, and 10 cm.

Remember to practice these constructions multiple times to develop your skills and accuracy in drawing precise geometric figures.