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Triangle Angle Bisectors Worksheets

Practice equal half-angles, incenter distances and right triangles with clear diagrams and worked answers.

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Find each requested angle or length. Use the equal angles and marked perpendicular distances.

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Follow the equal-angle and equal-distance marks

An angle bisector splits an angle into two equal parts. The three internal angle bisectors meet at the incenter C, which is equally distant from all three sides.

Learning objective

What this activity builds

Use angle bisectors and the incenter to find missing angles and segment lengths.

Worked example

An incenter is 13 units from a vertex and 5 units from the adjacent side. Find the length from the vertex to the perpendicular foot.

12 units.

The perpendicular segment makes a right triangle. The missing leg is sqrt(13² - 5²) = sqrt(144) = 12.

Teaching notes

Make the practice count

  • An angle bisector divides the whole angle into two equal angles.
  • The incenter is equally distant from all three sides; measure these distances perpendicularly.
  • Identify the hypotenuse before using the Pythagorean theorem.

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Eight diagrams progress from equal half-angles to incenter right triangles and equal perpendicular distances.

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Math SheetNameScoreTeacherDateTriangle Angle BisectorsUse equal angle halves, perpendicular incenter distances, and right-triangle relationships to find each missing measure.1. angle FDR = 63 deg. Find angle FDP.DFRPangle FDP =2. angle NXQ = 60 deg. Find angle NXE.XNEQangle NXE =3. CH = 6 and RC = 10. Find RH.RTZHIUCRH =4. CN = 8 and EN = 20. Find EC.EPLNYBCEC =Angle bisectors meet at the incenter, which is equally distant from all three sides.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateTriangle Angle BisectorsUse equal angle halves, perpendicular incenter distances, and right-triangle relationships to find each missing measure.5. CJ = 10 and FJ = 17. Find FC.FYUJMZCFC =6. CQ = 4 and TQ = 9. Find TC.TJPQKBCTC =7. CX = 12. Find CJ.FMYXJACCJ =8. CB = 4 and RC = 12. Find RB.RXABMYCRB =Angle bisectors meet at the incenter, which is equally distant from all three sides.math-sheet.comPage 2 of 2

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