Perpendicular Bisectors and Circumcircle
Learn how to construct perpendicular bisectors using a compass, and use them to find the circumcentre of a triangle. Let’s get started! 🚀
Video Lesson
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Flashcards
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🛎️ What Is a Perpendicular Bisector?
- A perpendicular bisector cuts a line segment in half.
- It meets the segment at a right angle (90°) at the midpoint.
🛎️ Drawing a Perpendicular Bisector
- With a compass, set the width greater than half the segment.
- Draw arcs above and below from both ends, keeping the same width.
- Draw a straight line through the two points where the arcs cross.
🛎️ Key Property of a Perpendicular Bisector
- Every point on the perpendicular bisector is the same distance from both ends of the line segment.
- This helps you find points that are exactly in the middle between the two ends.
🛎️ Perpendicular Bisectors and the Circumcentre
- The circumcentre is where the three perpendicular bisectors of a triangle meet.
- It is equal distance from all three vertices and is the centre of the circumcircle.
Practice Questions
Test your understanding
What is a perpendicular bisector?
Correct! 🎉 +10 pointsNot quite right
A perpendicular bisector is a line that cuts a segment into two equal parts at a right angle.
Which tool is used to construct the perpendicular bisector of a segment?
Correct! 🎉 +10 pointsNot quite right
The ruler helps us draw straight lines and measure lengths, while the compass allows us to create equal-length arcs from each endpoint of the segment. This helps us find the midpoint and draw a perpendicular line through it.
How do you find the circumcentre of a triangle?
Correct! 🎉 +20 pointsNot quite right
To find the circumcentre, you need to draw the perpendicular bisectors of at least two sides of the triangle. Their intersection point is the circumcentre.
What is the circumcentre of a triangle?
Correct! 🎉 +20 pointsNot quite right
The circumcentre of a triangle is the point that is equidistant from all three vertices of the triangle. It is the centre of the circle that passes through all three vertices (circumcircle).
What does the circumcircle of a triangle pass through?
Correct! 🎉 +20 pointsNot quite right
The circumcircle passes through all three vertices of the triangle. It is the circle whose center is the circumcentre.
You're building a triangular park and want to place a fountain equidistant from all three corners. Which geometric point should you find?
Correct! 🎉 +30 pointsNot quite right
You need to find the circumcentre. The circumcentre is the point that is the same distance from all three vertices, making it the perfect location for the fountain.
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Perpendicular Bisectors and Circumcircle
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