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Chapter 5.1. Bisectors of Triangles. Concept. Use the Perpendicular Bisector Theorems. A. Find BC . BC = AC Perpendicular Bisector Theorem BC = 8.5Substitution. Answer: 8.5. Use the Perpendicular Bisector Theorems. B. Find XY . Answer: 6.

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Chapter 5.1

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Chapter 5.1

Bisectors of Triangles

Concept

Use the Perpendicular Bisector Theorems

A. Find BC.

BC= ACPerpendicular Bisector Theorem

BC= 8.5Substitution

Use the Perpendicular Bisector Theorems

B. Find XY.

Use the Perpendicular Bisector Theorems

C. Find PQ.

A. Find NO.

A.4.6

B.9.2

C.18.4

D.36.8

B. Find TU.

A.2

B.4

C.8

D.16

C. Find EH.

A.8

B.12

C.16

D.20

Concept

Use the Angle Bisector Theorems

A. Find DB.

DB= DCAngle Bisector Theorem

DB= 5Substitution

Use the Angle Bisector Theorems

B. Find mWYZ.

Use the Angle Bisector Theorems

C. Find QS.

Answer: So, QS = 4(3) – 1 or 11.

A. Find the measure of SR.

A.22

B.5.5

C.11

D.2.25

B. Find the measure of HFI.

A.28

B.30

C.15

D.30

C. Find the measure of UV.

A.7

B.14

C.19

D.25

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 mSPU if S is the incenter of ΔMNP.

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

A.12

B.144

C.8

D.65