1. Warm Up 11.29.11 Week 7 Label the information: AB C D 1) ∠C is a right angle. 2) ∠A ≅ ∠B 3) AB = 8 4) bisects

2. Re 1 A B P C If C is on the perp bisector then CA = CB. If DA = DB, then D is on the perp bisector. D

3. m Geometry 5.1 Day 2 I will use properties of perpendicular bisectors. The length of the perpendicular segment from the point to the line. Distance from point to line Ex 1 P Q The distance between Q and the line m is QP.

4. Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Theorem 5.3 If m ∠BAD = m∠CAD, then DB = DC. A B C D

5. A B C D Angle Bisector Theorem Converse If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. Theorem 5.4 If DB = DC, then m∠BAD = m∠CAD.

6. Ex 2 Prove that DB = DC Reflexive Property A B C D ≅ ∆BAD ≅ ∆CAD AAS ≅ CPCSC DB = DC Definition of Congruent Segments DA bisects ∠BAC Definition of Bisector ∠BAD ≅ ∠CAD

7. Do 1 : Prove that ML = MN. L M N P Handout - 5.1B Assignment is the bisector of ∠LPN.