Angles in Same Segment (Motivate) MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz focuses on Unit IV: Geometry, specifically the topic Angles in Same Segment. It covers concepts where equal angles subtend the same chord or segment. Complete the 10 multiple-choice questions to test your understanding, check your score immediately, and download the answer key PDF for revision.
Understanding Angles in the Same Segment
In the geometry of circles, a segment is a region bounded by a chord and the arc subtended by the chord. The theorem states that angles subtended by the same arc at the circumference are equal. This is often phrased as “Angles in the same segment of a circle are equal.”
Key Concepts
- The Theorem: If points A and B are on a circle, and points C and D are also on the circle such that C and D are on the same side of chord AB, then Angle ACB is equal to Angle ADB.
- Motivation: This property can be motivated by observing that the angle at the center is double the angle at any point on the remaining part of the circle. Since the center angle is fixed for a given arc, all angles at the circumference must be equal.
- Semicircle Property: An important corollary is that the angle in a semicircle is a right angle (90 degrees).
- Cyclic Points: Points lying on the same circle are called concyclic points.
Quick Summary Table
| Property | Description |
|---|---|
| Angles in Same Segment | Are always equal to each other. |
| Angle in Semicircle | Always 90 degrees (Right Angle). |
| Angle at Center | Twice the angle at the circumference subtended by the same arc. |
| Major Segment Angle | Always an acute angle. |
Additional Practice Questions
- If an angle in a segment is 45 degrees, what is the angle subtended by the same arc at the center? (Ans: 90 degrees)
- Can an angle in a minor segment be obtuse? (Ans: Yes)
- If points P, Q, R, S are concyclic and lying on a circle, and Angle PQS = Angle PRS, what does this imply? (Ans: They are angles in the same segment).
- What is the sum of angles in the same segment? (Ans: This question is invalid as they are equal individually, not summed typically).
- Does the radius length affect the equality of angles in the same segment? (Ans: No, the property holds regardless of size).
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.