Geometry Quadrilaterals & Polygons 1 — Questions and Answers
Question 1: What is a quadrilateral?
- A polygon with three sides.
- A polygon with four sides (Correct answer)
- A polygon with five sides.
- A circle.
Correct answer: A polygon with four sides
A quadrilateral is a fundamental type of polygon, specifically defined as a closed two-dimensional shape with exactly four straight sides and four vertices. Examples include squares, rectangles, rhombuses, and trapezoids. The term 'quad' means four, directly indicating its number of sides.
Question 2: Which of the following is a type of quadrilateral?
- Triangle.
- Pentagon.
- Rectangle (Correct answer)
- Hexagon.
Correct answer: Rectangle
A rectangle is a specific type of quadrilateral, meaning it is a polygon with four sides. It is characterized by having four right angles (90 degrees) and opposite sides that are equal in length and parallel. Other quadrilaterals include squares, rhombuses, and trapezoids.
Question 3: What is a polygon?
- A shape with curves.
- A closed figure with straight line segments (Correct answer)
- A figure with no sides.
- A three-dimensional shape.
Correct answer: A closed figure with straight line segments
A polygon is a closed two-dimensional shape made up entirely of straight line segments. These segments, called sides, connect at points called vertices, and each side intersects exactly two other sides. This definition excludes shapes with curves or open figures.
Question 4: How many sides does a hexagon have?
- Five.
- Six (Correct answer)
- Seven.
- Eight.
Correct answer: Six
The prefix 'hexa-' in hexagon directly indicates the number six. Therefore, a hexagon is a polygon that is defined by having exactly six straight sides and six interior angles. Examples include regular hexagons, where all sides and angles are equal, and irregular hexagons.
Question 5: Which quadrilateral has all sides equal and all angles equal?
- Rectangle.
- Square (Correct answer)
- Rhombus.
- Trapezoid.
Correct answer: Square
A square is a special type of quadrilateral that possesses two key properties: all four of its sides are equal in length, and all four of its interior angles are right angles (90 degrees). This makes it both a rhombus (all sides equal) and a rectangle (all angles 90 degrees).
Question 6: What defines a parallelogram?
- All sides are equal.
- Opposite sides are parallel and equal (Correct answer)
- Only one pair of parallel sides.
- All angles are right angles.
Correct answer: Opposite sides are parallel and equal
A parallelogram is a quadrilateral characterized by having two pairs of parallel sides. A key property is that its opposite sides are not only parallel but also equal in length, and its opposite angles are equal. Rectangles, squares, and rhombuses are all specific types of parallelograms.
Question 7: What is the sum of interior angles of a quadrilateral?
- 180 degrees.
- 270 degrees.
- 360 degrees (Correct answer)
- 540 degrees.
Correct answer: 360 degrees
The sum of the interior angles of any quadrilateral is always 360 degrees. This property holds true for all types of quadrilaterals, whether they are regular or irregular, convex or concave. This can be understood by dividing any quadrilateral into two triangles, each having an angle sum of 180 degrees.
Question 8: Which polygon has five sides?
- Triangle.
- Pentagon (Correct answer)
- Hexagon.
- Heptagon.
Correct answer: Pentagon
A pentagon is a polygon specifically defined by having five straight sides and five interior angles. The prefix 'penta-' means five, directly indicating its number of sides. A regular pentagon has all sides and all angles equal.
Question 9: Which shape is classified as a regular polygon?
- Rectangle.
- Regular hexagon (Correct answer)
- Scalene triangle.
- Trapezoid.
Correct answer: Regular hexagon
A regular polygon is a polygon that is both equilateral (all sides are equal in length) and equiangular (all interior angles are equal in measure). A regular hexagon fits this definition perfectly, as all six of its sides are equal and all six of its interior angles are equal. Rectangles, scalene triangles, and trapezoids are generally not regular polygons unless specific conditions are met (e.g., a square is a regular rectangle).
Geometry Quadrilaterals & Polygons 1
What is a quadrilateral?