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5.3 – Use Angle Bisectors of Triangles

5.3 – Use Angle Bisectors of Triangles. Remember that an angle bisector is a ray that divides an angle into two congruent adjacent angles. Remember also that the distance from a point to a line is the length of the perpendicular segment from the point to the line.

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5.3 – Use Angle Bisectors of Triangles

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  1. 5.3 – Use Angle Bisectors of Triangles Remember that an angle bisector is a ray that divides an angle into two congruent adjacent angles. Remember also that the distance from a point to a line is the length of the perpendicular segment from the point to the line.

  2. 5.3 – Use Angle Bisectors of Triangles In the diagram, Ray PS is the bisector of <QPR and the distance from S to Ray PQ is SQ, where Segment SQ is perpendicular to Ray PQ.

  3. 5.3 – Use Angle Bisectors of Triangles

  4. 5.3 – Use Angle Bisectors of Triangles 42 Example 1: Find the measure of <GFJ.

  5. 5.3 – Use Angle Bisectors of Triangles He is equidistant to both sides by the Angle Bisector Theorem. Example 2: Three spotlights from two congruent angles. Is the actor closer to the spotlighted area on the right or on the left?

  6. 5.3 – Use Angle Bisectors of Triangles Example 3: For what value of x does P lie on the bisector of <A? x+3=2x-1 3=x-1 4=x

  7. 5.3 – Use Angle Bisectors of Triangles 11 5 Example 4: Find the value of x.

  8. 5.3 – Use Angle Bisectors of Triangles

  9. 5.3 – Use Angle Bisectors of Triangles The point of concurrency of the three angle bisectors of a triangle is called the incenter of the triangle. The incenter always lies inside the triangle.

  10. 5.3 – Use Angle Bisectors of Triangles Example 5: In the diagram, N is the incenter of Triangle ABC. Find ND. c2=a2+b2 202=NF2+162 400=NF2+256 144= NF2 NF=12 Because NF=ND, ND=12.

  11. 5.3 – Use Angle Bisectors of Triangles Example 6: In the diagram, G is the incenter of Triangle RST. Find GW.

  12. Now you try  • p313 • 3-6, 9,10,12,13,15,19 • HW: p313 • 8,11,14,16,18,20

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