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Warm Up

Week 7. Warm Up. 11.30.11. Tell if the geometric figure can have a bisector. 1) angle. 2) ray. 3) line. 4) segment. 5) point. Perp Bisector of a Triangle. A line ( or ray or segment ) that is perpendicular to a side of a triangle at the midpoint of that side.

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Warm Up

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  1. Week 7 Warm Up 11.30.11 Tell if the geometric figure can have a bisector. 1)angle 2) ray 3) line 4) segment 5) point

  2. Perp Bisector of a Triangle A line ( or ray or segment ) that is perpendicular to a side of a triangle at the midpoint of that side. Perp Bisector Ex 1

  3. Concurrent Lines Lines that intersect at the same point. Ex 2 Point of concurrency can be in, on, or outside the triangle. Rule 1

  4. Theorem 5.5 F E • • D G • DE = DF = DG

  5. B Ex 3 C A • D DA = DB = DC

  6. Angle Bisector of a Triangle Three angle bisectors meet at point of concurrency. Ex 4 Incenter • Incenter The point of concurrency, and it always lies inside the triangle.

  7. Theorem 5.6 F E P D PD = PE = PF

  8. Ex 5 What is the length of LR? M T5.6 ≅ ≅ 15 17 R a2 + b2 = c2 P S N L ( NQ )2 + ( LQ )2 = ( LN )2 ≅ so 152 + ( LQ )2 = 172 Q LR = 8. 225 + ( LQ )2 = 289 ( LQ )2 = 64 LQ = 8

  9. Do 1 : What is the distance from L to P? M 3 R 4 P S N L Q Assignment Handout - 5.2B

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