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Perpendicular Bisectors and Circumcircle

Geometry and Measures Perpendicular Bisectors and Circumcircle

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(0:01) What is Perpendicular Bisector?: A perpendicular bisector is a line that cuts a line segment exactly in half and meets it at a 90-degree angle.
(0:34) How to Construct a Perpendicular Bisector? Method 1: Use a ruler to locate the midpoint, then draw a perpendicular line through it. Method 2: Use a compass to draw two equal-length arcs from each endpoint of the segment. Then, draw a straight line through the 2 points of intersection.
(1:23) Key Property of Perpendicular Bisectors: Any point on the perpendicular bisector of a line segment is equidistant from the two endpoints of the line segment.
(1:38) How to Find the Circumcenter of a Triangle: Construct perpendicular bisectors for at least two sides of the triangle; their intersection point is the circumcenter, which is equidistant from all 3 vertices.

📂 Revision Cards

Perpendicular bisector dividing a line segment at a 90-degree angle with midpoint marked. — 1) Perpendicular Bisector Definition

Instructions for drawing a perpendicular bisector with a ruler and a compass. — 2) How to Construct a Perpendicular Bisector

Diagram of a triangle’s circumcentre, showing the circumradius, circumscribed circle (circumcircle), and the intersection of perpendicular bisectors. — 3) Circumcenter, Circumradius, and Circumcircle

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Perpendicular Bisectors and Circumcircle

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Q: What is a perpendicular bisector?

A line that divides a segment into two equal parts

A line that connects the midpoint of a segment to one of its endpoints

A line that forms an acute angle with a segment

A line that divides a segment into two equal parts at a right angle

Feedback: Not quite! A perpendicular bisector is a line that cuts a segment into two equal parts at a right angle.

Feedback: Well done! A perpendicular bisector is a line that cuts a segment into two equal parts at a right angle.

2 / 6

Q: Which tool is used to construct the perpendicular bisector of a segment?

An eraser

A calculator

A ruler and compass

A stapler

Feedback: Not quite! 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.

Feedback: Well done! 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.

3 / 6

Q: How do you find the circumcenter of a triangle?

Draw a perpendicular bisector for each side of the triangle

Use a compass to find the center of the triangle

Find the midpoint of the longest side

Draw an altitude from each vertex

Feedback: Not quite! To find the circumcenter, you need to draw the perpendicular bisectors of at least two sides of the triangle. Their intersection point is the circumcenter.

Feedback: Well done! To find the circumcenter, you need to draw the perpendicular bisectors of at least two sides of the triangle. Their intersection point is the circumcenter.

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Q: What is the circumcenter of a triangle?

The point equidistant from all three sides

The point equidistant from all three vertices

The midpoint of the longest side

Feedback: Not quite! The circumcenter of a triangle is the point that is equidistant from all three vertices of the triangle. It is the center of the circle that passes through all three vertices (circumcircle).

Feedback: Well done! The circumcenter of a triangle is the point that is equidistant from all three vertices of the triangle. It is the center of the circle that passes through all three vertices (circumcircle).

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Q: What does the circumcircle of a triangle pass through?

The midpoints of the sides of the triangle

The circumcenter of the triangle

The vertices of the triangle

Feedback: Not quite! The circumcircle passes through all three vertices of the triangle. It is the circle whose center is the circumcenter.

Feedback: Well done! The circumcircle passes through all three vertices of the triangle. It is the circle whose center is the circumcenter.

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Q: You’re building a triangular park and want to place a fountain equidistant from all three corners. Which geometric point should you find?

The incenter

The centroid

The circumcenter

The orthocenter

Feedback: Not quite! You need to find the circumcenter. The circumcenter is the point that is the same distance from all three vertices, making it the perfect location for the fountain.

Feedback: Well done! You need to find the circumcenter. The circumcenter is the point that is the same distance from all three vertices, making it the perfect location for the fountain.

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