Set 2: Challenging Practice Questions for Constructions

Title: Set 2: Challenging Practice Questions for Constructions

Question 1:
Imagine you are an architect designing a new park. You want to create a walking path that connects two points, A and B, in a straight line. Using only a compass and a ruler, construct a line segment AB that is 8 cm long.

Answer 1:
To construct a line segment AB that is 8 cm long, follow these steps:
1. Draw a point A on your paper.
2. Use the compass to measure 8 cm and draw an arc above and below point A.
3. Without changing the compass width, place the compass on the intersection of the arcs and draw two more arcs that intersect the first arcs.
4. Use the ruler to draw a straight line connecting point A to point B, which is the intersection of the arcs.

Question 2:
You are designing a garden in the shape of a square. The garden needs to have an area of 64 square meters. Using only a compass and a ruler, construct a square garden with the desired area.

Answer 2:
To construct a square garden with an area of 64 square meters, follow these steps:
1. Draw a point A on your paper.
2. Use the compass to measure the square root of 64 (which is 8) and draw an arc above and below point A.
3. Without changing the compass width, place the compass on the intersection of the arcs and draw two more arcs that intersect the first arcs.
4. Use the ruler to draw lines connecting the points of intersection, forming a square.

Question 3:
You are planning to build a bridge over a river. The bridge needs to be perpendicular to the river bank. Using only a compass and a ruler, construct a line that is perpendicular to the given line.

Answer 3:
To construct a line perpendicular to a given line, follow these steps:
1. Draw the given line on your paper.
2. Place the compass on a point along the given line and draw an arc above and below the line.
3. Without changing the compass width, place the compass on the other point along the line and draw two more arcs that intersect the first arcs.
4. Use the ruler to draw a straight line connecting the points of intersection. This line will be perpendicular to the given line.

Question 4:
Imagine you are building a house and need to construct a right-angled triangle with one side measuring 5 cm and the hypotenuse measuring 10 cm. Using only a compass and a ruler, construct the right-angled triangle.

Answer 4:
To construct a right-angled triangle with one side measuring 5 cm and the hypotenuse measuring 10 cm, follow these steps:
1. Draw a line segment AB of length 10 cm.
2. Using the compass, draw an arc with center A and radius 5 cm.
3. Using the compass, draw an arc with center B and radius 10 cm.
4. Connect the points of intersection of the two arcs with a straight line. This line will form the third side of the right-angled triangle.

Great job practicing these challenging construction questions! Remember, don't be discouraged if you find them difficult at first. Break down the problems, use multiple approaches, and think creatively to find the solutions. Keep practicing, and you'll become a construction expert in no time!