📚 Topic Summary
A cyclic quadrilateral is a four-sided figure whose vertices all lie on a single circle. This means the quadrilateral can be inscribed within a circle. A key property of cyclic quadrilaterals is that their opposite angles are supplementary, meaning they add up to 180 degrees. Understanding this property unlocks a lot of problem-solving potential! This worksheet will help you learn all about it.
🧠 Part A: Vocabulary
Match the term with its definition:
- Circle
- Cyclic Quadrilateral
- Inscribed Angle
- Supplementary Angles
- Vertex
- The point where two or more lines or edges meet.
- Angles whose measures add up to 180 degrees.
- A quadrilateral whose vertices all lie on a single circle.
- A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
- An angle formed by two chords in a circle that have a common endpoint.
✍️ Part B: Fill in the Blanks
A quadrilateral is considered ________ if all its vertices lie on the ________ of a circle. The ________ angles of a cyclic quadrilateral are always ________, adding up to 180 degrees. This property is key to solving many problems related to ________ quadrilaterals.
🤔 Part C: Critical Thinking
Explain in your own words why knowing that a quadrilateral is cyclic can help you find missing angles.