Angle Bisectors and Incircle
Learn how to construct angle bisectors using a compass, and use them to draw a triangle’s incircle. Let’s get started! 🚀
Video Lesson
Watch and learn the basics
Flashcards
Review key concepts visually
%20Angle%20Bisector.webp)
%20Drawing%20Angle%20Bisectors.webp)
%20Angle%20Bisector%20Property.webp)
%20Triangle%20Incircle.webp)
🛎️ What Is an Angle Bisector?
- An angle bisector splits an angle into two equal parts.
- Each new angle is exactly half of the original angle.
🛎️ How to Draw an Angle Bisector?
- You can draw an angle bisector using a protractor by halving the angle.
- You can also use a compass to draw the bisector without measuring.
🛎️ The Key Property of an Angle Bisector
- Any point on an angle bisector is equidistant from both sides of the angle.
- This means the perpendicular distance to each side is the same.
🛎️ Incentre and Incircle
- The incentre is where the three angle bisectors of a triangle meet.
- The incircle is the largest circle that fits inside the triangle and touches all three sides.
Practice Questions
Test your understanding
What is an angle bisector?
Correct! 🎉 +10 pointsNot quite right
An angle bisector is a line or ray that divides an angle into two equal parts.
What tool is commonly used to construct an angle bisector?
Correct! 🎉 +10 pointsNot quite right
To construct an angle bisector, you can use a protractor to measure the angle, or a compass to draw arcs and bisect the angle accurately.
What is the incentre of a triangle?
Correct! 🎉 +20 pointsNot quite right
The incentre is the point where the angle bisectors of a triangle intersect.
What is the inradius of a triangle?
Correct! 🎉 +20 pointsNot quite right
The inradius is the distance from the incentre to any side of the triangle. This distance is the same for all three sides.
If you want to draw the incircle of a triangle, what do you need to know?
Correct! 🎉 +20 pointsNot quite right
To draw the incircle, you need to know the location of the incentre (where the angle bisectors meet) and the inradius (the distance from the incentre to any side).
To find the largest circle that you can cut out of a triangle piece of paper, what should you do?
Correct! 🎉 +30 pointsNot quite right
To find the largest circle that fits inside a triangle, you need to find the incircle. This is done by drawing the angle bisectors to locate the incentre, then measuring the distance from it to any side to determine the inradius.
Want to see the full working?
Interactive Activity
Explore angle bisector construction and how they form a triangle's incircle
Loading interactive widget...
Click here to open ChatCat