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Cyclic Quadrilaterals
Circle Theorem: Opposite angles in a cyclic quadrilateral add up to 180°
- This theorem explains that in a cyclic quadrilateral, if all four vertices lie on the circumference of a circle, then the angles opposite to each other will sum up to 180°.
- A cyclic quadrilateral must have all its vertices on the circumference of a circle.
- The cyclic quadrilateral theorem is exclusive to cyclic quadrilaterals and does not apply to other types of quadrilaterals within a circle.
- For instance, a common scenario that does not involve a cyclic quadrilateral is depicted below:
- When utilizing the cyclic quadrilateral theorem as a reason in an examination, it is essential to incorporate key vocabulary.
- In this context, opposite angles in a cyclic quadrilateral sum up to 180°.
- The term 'supplementary' denotes angles that add up to 180° and can also be utilized with specific reference to angles within a cyclic quadrilateral.
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FAQs on Cyclic Quadrilaterals - Mathematics for GCSE/IGCSE - Class 10
| 1. How can I identify a cyclic quadrilateral? |  |
Ans. A cyclic quadrilateral is a quadrilateral where all four vertices lie on the circumference of a circle. To identify a cyclic quadrilateral, you can check if the sum of opposite angles is equal to 180 degrees.
| 2. What is the Cyclic Quadrilateral Theorem? | |
Ans. The Cyclic Quadrilateral Theorem states that the opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.
| 3. Can a quadrilateral be cyclic if all its sides are equal? | |
Ans. No, a quadrilateral with all sides equal is a rhombus, and not all rhombuses are cyclic quadrilaterals. A cyclic quadrilateral requires all four vertices to lie on the circumference of a circle.
| 4. How do I prove that a quadrilateral is cyclic? | |
Ans. To prove that a quadrilateral is cyclic, you can show that the sum of opposite angles is 180 degrees. Another method is to show that the quadrilateral can be inscribed in a circle.
| 5. Why is understanding cyclic quadrilaterals important in mathematics? | |
Ans. Understanding cyclic quadrilaterals is important in geometry as it helps in solving problems related to angles and circles. It also helps in proving theorems and properties of quadrilaterals.
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