Linear Pair Axiom (Motivate) MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz focuses on Unit IV: Geometry, specifically the Linear Pair Axiom. The questions cover concepts where a ray stands on a line and the sum of adjacent angles is 180 degrees. Test your understanding of these fundamental axioms, check your score immediately, and download the solution PDF for revision.
Concept Overview: Linear Pair Axiom
In Class IX Geometry (Unit IV), the Linear Pair Axiom is a fundamental concept used to prove many subsequent theorems. It deals with the relationship between angles formed when a ray stands on a straight line.
Axiom 1: Ray on a Line
If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degrees. This pair of angles is called a linear pair.
- Condition: The angles must be adjacent (share a common vertex and a common arm).
- Condition: The non-common arms must form a line (opposite rays).
- Result: Angle 1 + Angle 2 = 180 degrees.
Axiom 2: Converse of Linear Pair Axiom
If the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line.
This converse axiom is crucial for proving that three points are collinear or that a given geometric figure involves a straight line.
Quick Comparison
| Property | Adjacent Angles | Linear Pair |
|---|---|---|
| Common Vertex | Yes | Yes |
| Sum of Angles | Any value | Always 180 degrees |
| Non-common arms | Any position | Form a straight line |
Important Notes for Calculations
- If the ratio of two angles in a linear pair is given (e.g., a:b), assume the angles are ax and bx. Then ax + bx = 180.
- Bisectors of a linear pair always form a right angle (90 degrees).
- Two acute angles cannot form a linear pair (Sum would be less than 180).
- Two obtuse angles cannot form a linear pair (Sum would be greater than 180).
Extra Practice Questions
- Find the measure of an angle which is 30 degrees less than its supplement.
- Two lines AB and CD intersect at O. If angle AOC = 50 degrees, find angle BOD and angle BOC.
- In a linear pair, if one angle is 3 times the other, find the angles.
- Prove that the bisectors of the angles of a linear pair are at right angles.
- If a ray stands on a line such that adjacent angles are x + 10 and x – 10, find x.
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