Test: Construction Of Polygons - Grade 9 MCQ

A rhombus is defined by having all sides equal and diagonals that bisect each other at right angles. This unique property allows for various geometric constructions and proofs involving rhombuses.

A rectangle must have angles of 90° at each vertex. This right angle is crucial for ensuring that the opposite sides are both equal and parallel, fulfilling the definition of a rectangle.

When constructing a square from a rhombus, all angles must be made right angles. This adjustment transforms the rhombus into a square, ensuring that all properties of equal sides and right angles are satisfied.

In a parallelogram, opposite sides are parallel. This characteristic is fundamental to the definition of parallelograms, ensuring that the shape has equal opposite sides and helps in maintaining the properties of angles and diagonals.

A square has all sides equal and diagonals that bisect each other at right angles. This unique combination of properties makes the square a fundamental shape in geometry, often used in various applications from architecture to art.

One effective method to construct a regular hexagon is by using interior angles, specifically constructing 120° angles at each vertex. This ensures that all sides are equal and that the shape retains its regularity.

The first step is to construct the first triangle using the three sides, including the given diagonal. This triangle serves as the foundation for the quadrilateral, allowing the remaining parts to be added accurately.

The diagonals of a rhombus bisect each other at right angles, which is a key property. This characteristic ensures that the rhombus maintains its symmetry and equal side lengths, aiding in accurate constructions.

To begin constructing a rectangle with one side and one diagonal, you construct a right-angled triangle using the given side and diagonal. This method ensures that the angles and side lengths are correctly proportioned to form a rectangle.

The first step in constructing a quadrilateral with four sides and one angle is to draw one side as the base. This provides a starting point for the construction, allowing the other sides and angles to be accurately positioned relative to this base.

The first step is to draw the first given angle at one end of the base. After this, the adjacent side is measured, and the second angle is constructed at the other end of the base, allowing for the completion of the quadrilateral.

The angle measure between the diagonals of a regular hexagon is 120°. This is due to the internal angles of the regular hexagon, which directly influence the angles formed by its diagonals.

When constructing a trapezium, one pair of sides must be parallel. This is the defining characteristic of a trapezium, differentiating it from other quadrilaterals and ensuring its unique properties.

In constructing a trapezium, it is typical to draw the parallel side first. This establishes the base for measuring the lengths of the other sides and ensures that the trapezium maintains its defining properties.

A regular hexagon has six equal sides. This property contributes to its symmetry and makes it a common shape in various geometric applications, including tiling and design.

When constructing a trapezium with the lengths of all four sides, it is essential that one pair of sides must be parallel. This characteristic defines the trapezium and is necessary for its proper geometric representation.

The first action is to construct a triangle with the two given sides and the included angle. This triangle serves as the basis for completing the parallelogram by constructing another triangle with equal side lengths.

The construction method that involves drawing multiple 60° angles is using central angles. Each side of the regular hexagon subtends an angle of 60° at the center of the circumcircle, allowing for accurate placement of vertices when constructing the shape.

The primary tools used for constructing polygons are a ruler and a compass. These tools allow for precise measurements and angles, making it possible to create various geometric shapes accurately. Using a ruler helps in drawing straight lines, while a compass is essential for creating arcs and circles, which are fundamental in polygon construction.

Both rectangles and parallelograms have diagonals that bisect each other. This property is important for understanding the internal structure and symmetry of these shapes, facilitating various geometric constructions.