Respuesta :
D. The square construction will need three arcs along the circle, but the equilateral triangle construction will
need two arcs above and the two arc below the diameter of the circle.
need two arcs above and the two arc below the diameter of the circle.
For the square construction, the diameter will be used, but for the equilateral triangle construction, the radius will be used.
Option A is correct
How to construct a square?
A square is a closed, two-dimensional figure with four equal sides. The four angles of a square are also equal i.e. 90 degrees each. The only dimension we have been provided is the length of one side of a square i.e. 5 cm. We know that the interior angles of a square are at right angles or equal to 90 degrees. Hence, we do not require any other measurement for constructing a square. The measurement of the length of all the four sides of a square equal and perpendicular to each other. With the help of this information, we can now construct a square each of whose sides measure 5 cm.
How to construct a equilateral triangle?
Step 1: Draw a line segment YZ = 6 units.
Step 2: Use a ruler and measure 6 units with the compass. With Y as the center draw an arc above the line YZ.
Step 3: With Z as the center and without changing the measure of length taken in the compass draw another arc to intersect the previous arc.
Step 4: Join the points XY and XZ to get an equilateral triangle XYZ.
In construction of a square inscribed in a circle, the diameter of the circle is first constructed within the circle from a desired location of one of the vertices of the square.
The diameter of the circle has then intersected the circumference at two vertices of the square.
The perpendicular bisector of the above diameter is constructed to intersect the circumference of the circle at the remaining two vertices of the square.
The points of the intersection with the circumference is then joined with straight lines to complete the construction of the inscribed square.
For the triangle, the radius of the circle is used to draw arcs on the circumference starting from a desired point and using the previous arc intersection as the starting point for the next arc.
The every other point of intersection of the arc and the circumference are then joined to complete the construction of the inscribed triangle.
Difference between a square and an equilateral triangle
A square is a quadrilateral and it has 4 sides while a triangle has 3 sides.
A square has each angle as 90 degrees while the angles of an equilateral triangle is 60 degrees.
The square is made up of up four equal lines while an equilateral triangle is made up of 3 equal lines.
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