Basic Geometrical Ideas - Free MCQ Test with solutions, Class 6 1000+ Questions

• One angle is 122°


• The angles are supplementary

• Supplementary angles add up to 180°


• Let the other angle be x°


• So, 122° + x° = 180°


• x° = 180° - 122°


• x° = 58°

• The other angle is 58°

Therefore, the correct answer is option D: 58°.

The common endpoint where two rays meet to form an angle is called the vertex. This point serves as the starting point for both rays (or arms) that make up the angle, making it a fundamental concept in geometry for defining angles.

• Point in a Plane: When a point is given in a plane, it can be used as a starting point to draw lines.


• Definition of a Line: A line can be defined as a straight path that extends infinitely in both directions.


• Drawing Lines from a Point:
  
  
  
  • From a single point, an infinite number of lines can be drawn in a plane.
  
  
  • Each line drawn from the point will extend infinitely in both directions.
  
  
  • Therefore, the correct answer is Infinite (Option D).
  
  
  
  

An angle which measures greater than 180 degrees but less than 360 degrees is known as a reflex angle. 

• Definition: A plane is a flat surface that extends indefinitely in all directions without any curves or edges.


• Characteristics:
  
  
  
  • It has no thickness or boundaries.
  
  
  • It is defined by at least three non-collinear points.
  
  
  • It is infinite in all directions.
  
  
  
  


• Examples:
  
  
  
  • The surface of a table can be considered as a plane.
  
  
  • The floor of a room can also be viewed as a plane.
  
  
  
  


• Usage in Geometry:
  
  
  
  • Planes are fundamental concepts in geometry and are used to define points, lines, and other shapes.
  
  
  • Two distinct planes are either parallel or intersect at a line.
  
  
  
  

A chord of a circle is a straight line segment whose endpoints both lie on the circle. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse. The word chord is from the Latin chorda meaning bowstring.

• Definition of a right angle: A right angle is an angle that measures exactly 90 degrees. It is commonly denoted by the symbol ∠.


• Characteristics of a right angle:
  
  
  
  • It is formed when two lines are perpendicular to each other.
  
  
  • It divides a straight angle into two equal parts.
  
  
  • It is commonly seen in shapes like squares, rectangles, and triangles.
  
  
  
  


• Examples of right angles:
  
  
  
  • The corner of a book
  
  
  • The corner of a window
  
  
  • The shape of a square
  
  
  
  


• Importance of right angles:
  
  
  
  • Used in construction and engineering to ensure perpendicularity.
  
  
  • Helps in measuring and drawing accurate angles.
  
  
  • Found in everyday objects and shapes, making them easy to identify.
  
  
  
  

• Line Segment: A line segment is a part of a line that is bounded by two distinct endpoints.


• Extending a Line Segment: When a line segment is extended in two directions indefinitely from each of its two endpoints, it forms a new geometric object.


• Classification: The resulting object is classified as a line.


• Line: A line is a straight path that extends indefinitely in both directions without any endpoints.

• Extending a line segment in both directions results in a line because it continues infinitely in both directions.


• A line has no endpoints and is represented by a straight path that goes on indefinitely.


• Therefore, when a line segment is extended in two directions indefinitely, it becomes a line.

A plane is a flat, two-dimensional surface that extends infinitely far. When two points are joined using a straight line on a flat surface, it is the plane that is being referred to. The line is part of the plane, but it is not the surface itself. Similarly, a ray and an intersecting line are also components that exist within a plane, but they are not the surface itself..
Correct option is B. Plane

• Definition of a line segment: A line segment is a part of a line that is bounded by two distinct end points.


• Joining points to form a line segment: To form a line segment, we need to join two distinct points in space. These two points act as the end points of the line segment.


• Number of points required: Only two points are required to form a line segment. Any additional points beyond these two are not necessary for defining the line segment.


• Role of additional points: While additional points may lie on the line segment, they do not play a role in defining the segment itself. They are simply points that exist along the line segment.


• Conclusion: Therefore, the statement is correct in saying that any line segment can be formed by joining two points.

An obtuse angle is between 90° and 180°.

• Option A: ¹¹/₂₁ × 90° = 47.14° (acute)
• Option B: ⁸/₂₀ × 360° = 144° (obtuse)
• Option C: ¹¹/₂₁ × 360° ≈ 188.57° (reflex angle)
• Option D: ⁸/₂₀ × 90° = 36° (acute)

Only Option B results in an obtuse angle.

Two lines intersect when they cross each other. They form vertically opposite angles, which we will learn later. The point where the lines intersect is called the point of intersection.

A ruler's edge is used to draw straight lines between two points, which are defined as line segments in geometry.

Therefore, the correct answer is a line segment.

Acute angles measure less than 90 degrees

• Collinear points: Points that lie on the same straight line are called collinear points.


• Non-collinear points: Points that do not lie on the same straight line are called non-collinear points.


• When three or more points lie on the same line, they are known as collinear points.


• In the given options, option A: collinear is the correct term to describe points that lie on the same line.

• Definition: Complementary angles are two angles whose measures add up to 90 degrees.

• Option A: 120° and 60°


• Option B: 50° and 30°


• Option C: 65° and 25°


• Option D: 70° and 30°

• In order to find out which pair of angles are complementary, we need to check if their sum equals 90 degrees.


• Let's calculate the sum of angles for each option:




• Option A: 120° + 60° = 180° (Not complementary)


• Option B: 50° + 30° = 80° (Not complementary)


• Option C: 65° + 25° = 90° (Complementary)


• Option D: 70° + 30° = 100° (Not complementary)




• Therefore, the angles 65° and 25° from Option C are together classified as complementary angles.

• Definition: When two rays meet each other at a certain point, an angle is formed.


• Angle Formation: The point where the two rays meet is called the vertex of the angle, and the rays are called the arms of the angle.


• Measurement: Angles can be measured in degrees using a protractor.


• Types of Angles: There are various types of angles such as acute, obtuse, right, straight, and reflex angles.


• Importance: Angles play a crucial role in geometry and trigonometry, helping in measuring distances, determining shapes, and solving mathematical problems.

ANSWER :- d

Solution :- Two distinct lines intersect in at most one point; two distinct planes intersect in at most one line. If two coplanar lines do not intersect, they are parallel. Two lines which are not coplanar cannot intersect and are called "skew" lines. Two planes which do not intersect are parallel.

Explanation: Parallel lines are lines that do not intersect at any point and maintain a constant distance between them. They run in the same direction and never meet, no matter how far they are extended.