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Collection of angle bisector problems (30)
angle bisector problems on this website are free for educational use only. Commercial use is strictly forbidden. You may not sell, resell, sublicense, or redistribute these worksheets in any form for profit. Please read the full terms.
Triangle DEF with angle bisector EG, illustrating the Angle Bisector Theorem to find the length of DF.
Angle Bisector Theorem: In triangle PQR, if PS bisects angle P, then the ratio of sides a to b equals the ratio of segments x to y.
Prove: Angle Bisector Theorem — a geometric diagram demonstrating the relationship between the sides of a triangle divided by an angle bisector.
Angle Bisector Theorem: A ray bisecting an angle of a triangle divides the opposite side into segments proportional to the other two sides.
Solving for x in a geometry problem using angle bisector properties.
Geometric diagram illustrating angles with algebraic expression.
Right triangle with labeled sides and unknown segment.
Angle Bisector Theorem: An angle bisector divides the opposite side into segments proportional to the other two sides of the triangle.
The Triangle Angle Bisector Theorem states that an angle bisector divides the opposite side into segments proportional to the other two sides of the triangle.
Angle Bisector Theorem Converse: If a point is equidistant from the sides of an angle, it lies on the angle bisector.
Exterior Angle Bisector Theorem applied to find BD:BC ratio.
Triangle ABC with point P demonstrating proportional side ratios AB/BP = AC/CP.
The Angle Bisector Theorem, explaining how an internal angle bisector divides the opposite side in the ratio of the other two sides, with a proof and a sample problem.
Geometric diagram illustrating triangle ABC with angle bisector and proportional side lengths.
Example of an angle bisector in geometry, illustrating how a straight line divides angle ABC into two equal angles.
Geometric diagram of triangle ABC with point D on BC and line AD, illustrating angle at vertex A.
Diagram of two right triangles with labeled sides and angles.
Proof of the Angle Bisector Theorem using the sine rule, demonstrating the relationship between the sides and angles of triangle ABC.
Proof of the Angle Bisector Theorem using parallel lines and isosceles triangle properties.
Solving for x in a triangle using the Angle Bisector Theorem.
Geometric diagram showing triangle ABC with extended line and labeled angles.
Geometry problem involving triangle ABC with angle bisector AD and given side lengths.
Proof of Angle Bisector Theorem diagram with labeled points and angle bisector.
Find the length of BD in triangle ABC, given side lengths and angle θ.
Geometric diagram showing triangle ABC with extended line AE and labeled angles.
Triangle ABC with median CD dividing AB into segments AD = 12 and DB = x, where AC = 18 and BC = 24.
Geometry problem involving angle bisector and algebraic expressions in a triangle.
Geometry problem illustrating angle bisection, where AD bisects angle BAC, and the measure of angle DAC is 22.5°, resulting in angle BAC being 45°.
Triangle proportion diagram illustrating the relationship a/b = c/d with an altitude from vertex A to base BC.
Geometric diagram showing triangle ABC with a line segment AD and marked points.
Converse of the Angle Bisector Theorem: If a point is equidistant from the sides of an angle, then the point lies on the angle bisector.
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