1.5 Segment & Angle Bisectors

GeometryMrs. Blanco

Standard/Objective

Standard 3: Students will understand geometric concepts and applications.

Objectives:

• Find the Midpoint of a segment.

• Bisect a segment.

• Bisect an angle.

Midpoint• The point on a segment that divides the

segment into two congruent segments. (bisects a segment)

1 2 1 2,2 2

x x y y

Ex 1a: Find the midpoint of CD if C(-12,-9) & D(2,10).

12 2 9 10,

2 2

10 1,

2 2

15,2

Ex 1b: You Try:

Find the Midpoint of CDC(-1.5,4) & D(0.25,-1).

Ex 2a: The midpoint of BD is M(-1,1). One endpoint is D(2,6).

Find the coordinates of B.

D

M B(-4,-4)

Ex 2b: You Try:Find the B if M(0,3) & D(-8,-1)

Segment Bisector

• A segment, ray, line, or plane that intersects a segment at its midpoint.

A

BM

k

Angle BisectorAngle Bisector

• A ray that divides an angle into two adjacent angles that are congruent.

BD is an angle bisector of ABC.

B

A

C

D

Ex 3a: If QS bisects PQR & mSQR=22o, what is mPQR

and mPQS ?

mPQS=22°mPQR=44°

Ex 3b: If QS bisects PQR & mPQR=124o, what is mPQS

and mSQR ?

mPQS=62°mSQR=62°

x+40 = 3x-20

40 = 2x-20

60 = 2x

30 = x

Ex 4a: If RQ bisects PRS. Solve for x

m PRQ m QRSÐ = Ð

1/2x+20 = 3x-85

20 = 2 ½ x-85

105 = 2 ½ x

42 = x

Last Example:Ex 4b: If BD bisects ABC.

Solve for x

• Class practice—

• Pgs. 38-40

• #18, 22, 26, 28, 32, 38, 39, 40, 41, 44, 46, 48,

52, 54,