YOU NEED TO TAKE NOTES ON THIS!

Use the Perpendicular Bisector Theorems

A. Find the measure of BC.

Answer: 8.5

Use the Perpendicular Bisector Theorems

B. Find the measure of XY.

Answer: 6

Use the Perpendicular Bisector Theorems

C. Find the measure of PQ.

Answer: 7

A. A

B. B

C. C

D. D

A. 4.6

B. 9.2

C. 18.4

D. 36.8

A. Find the measure of NO.

A. A

B. B

C. C

D. D

A. 2

B. 4

C. 8

D. 16

B. Find the measure of TU.

A. A

B. B

C. C

D. D

A. 8

B. 12

C. 16

D. 20

C. Find the measure of EH.

• Special case - right triangles

In the special case of a right triangle, the circumcenter (C in the figure at right) lies exactly at the midpoint of the hypotenuse (longest side)

Use the Circumcenter Theorem

GARDEN A triangular-shaped garden is shown. Can a fountain be placed at the circumcenter and still be inside the garden?

By the Circumcenter Theorem, a point equidistant from three points is found by using the perpendicular bisectors of the triangle formed by those points.

Use the Circumcenter Theorem

Answer: No, the circumcenter of an obtuse triangle is in the exterior of the triangle.

Copy ΔXYZ, and use a ruler and protractor to draw the perpendicular bisectors. The location for the fountain is C, the circumcenter of ΔXYZ, which lies in the exterior of the triangle.

C

A. A

B. B

A. No, the circumcenter of an acute triangle is found in the exterior of the triangle.

B. Yes, circumcenter of an acute triangle is found in the interior of the triangle.

BILLIARDS A triangle used to rack pool balls is shown. Would the circumcenter be found inside the triangle?

Distance is always measured along a perpendicular line

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 WYZ.

Answer: mWYZ = 28

Use the Angle Bisector Theorems

C. Find QS.

Answer: So, QS = 4(3) – 1 or 11.

A. A

B. B

C. C

D. D

A. 22

B. 5.5

C. 11

D. 2.25

A. Find the measure of SR.

A. A

B. B

C. C

D. D

A. 28

B. 30

C. 15

D. 30

B. Find the measure of HFI.

A. A

B. B

C. C

D. D

A. 7

B. 14

C. 19

D. 25

C. Find the measure of UV.

Use the Incenter Theorem

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

Answer: SU = 6

Use the Incenter Theorem

Answer: SU = 6

Use the Incenter Theorem

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

Answer: mSPU = (62) or 31__12

A. A

B. B

C. C

D. D

A. 12

B. 144

C. 8

D. 65

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

A. A

B. B

C. C

D. D

A. 58°

B. 116°

C. 52°

D. 26°

B. Find the measure of BCD if D is the incenter of ΔACF.