Angle Bisector Theorem
A bisector divides the opposite side in proportion to adjacent sides.
Key idea
A bisector divides the opposite side in proportion to adjacent sides.
In depth
The bisector of an angle in a triangle divides the opposite side in the ratio of the adjacent sides: BD/DC = AB/AC. It follows from similar triangles or areas.
Worked example
Triangle with AB = 6, AC = 9, BC = 10: BD = 4 and DC = 6.
Formula
Real-world uses
- Dividing a triangular plot between two owners in proportion to road frontage
- Geometry proofs
Common mistake
Setting up the ratio with the wrong adjacent sides.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Angle Bisector Theorem?
A bisector divides the opposite side in proportion to adjacent sides. It is a topic at the advanced level in Geometry.
What is the formula for Angle Bisector Theorem?
The key formula is BD/DC = AB/AC.
Where is Angle Bisector Theorem used in real life?
Real-world examples: Dividing a triangular plot between two owners in proportion to road frontage; Geometry proofs.
What should I learn before Angle Bisector Theorem?
Make sure you are comfortable with Compass and Straightedge, the previous topic in Geometry.
What is a common mistake with Angle Bisector Theorem?
Setting up the ratio with the wrong adjacent sides.
How can I practise Angle Bisector Theorem?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Angle Bisector Theorem?
Move on to Medians and Centroid next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.