Chapter 5.1Bisectors of Triangles

Concept

Use the Perpendicular Bisector Theorems

A. Find BC.

Answer: 8.5

BC = AC Perpendicular Bisector Theorem

BC = 8.5 Substitution

Use the Perpendicular Bisector Theorems

B. Find XY.

Answer: 6

Use the Perpendicular Bisector Theorems

C. Find PQ.

Answer: 7

A. 4.6

B. 9.2

C. 18.4

D. 36.8

A. Find NO.

A. 2

B. 4

C. 8

D. 16

B. Find TU.

A. 8

B. 12

C. 16

D. 20

C. Find EH.

Concept

Concept

Use the Angle Bisector Theorems

A. Find DB.

Answer: DB = 5

DB = DC Angle Bisector Theorem

DB = 5 Substitution

Use the Angle Bisector Theorems

B. Find mWYZ.

Use the Angle Bisector Theorems

C. Find QS.

Answer: So, QS = 4(3) – 1 or 11.

A. 22

B. 5.5

C. 11

D. 2.25

A. Find the measure of SR.

A. 28

B. 30

C. 15

D. 30

B. Find the measure of HFI.

A. 7

B. 14

C. 19

D. 25

C. Find the measure of UV.

Concept

Use the Incenter Theorem

A. Find ST if S is the incenter of ΔMNP.

By the Incenter Theorem, since S is equidistant from the sides of ΔMNP, ST = SU.

Find ST by using the Pythagorean Theorem.

Use the Incenter Theorem

B. Find mSPU if S is the incenter of ΔMNP.

A. 12

B. 144

C. 8

D. 65

A. Find the measure of GF if D is the incenter of ΔACF.