Warm Up 11.29.11Week 7

Label the information:

A B

C

D•

1) ∠C is a right angle.

2) ∠A ≅ ∠B

3) AB = 8

4) bisects

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

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.

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•

A

B

C

D

Angle Bisector Theorem ConverseIf 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.

•

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

Do 1 :

Prove that ML = MN.

L

M

N

P

Handout - 5.1B Assignment

is the bisector of ∠LPN.