vocabulary you need to take notes on this!. concept
TRANSCRIPT
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Use the Perpendicular Bisector Theorems
A. Find the measure of BC.
Answer: 8.5
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Use the Perpendicular Bisector Theorems
B. Find the measure of XY.
Answer: 6
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Use the Perpendicular Bisector Theorems
C. Find the measure of PQ.
Answer: 7
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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.
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A. A
B. B
C. C
D. D
A. 2
B. 4
C. 8
D. 16
B. Find the measure of TU.
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A. A
B. B
C. C
D. D
A. 8
B. 12
C. 16
D. 20
C. Find the measure of EH.
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• 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)
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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.
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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
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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?
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Distance is always measured along a perpendicular line
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Use the Angle Bisector Theorems
A. Find DB.
Answer: DB = 5
DB = DC Angle Bisector Theorem
DB = 5 Substitution
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Use the Angle Bisector Theorems
B. Find WYZ.
Answer: mWYZ = 28
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Use the Angle Bisector Theorems
C. Find QS.
Answer: So, QS = 4(3) – 1 or 11.
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A. A
B. B
C. C
D. D
A. 22
B. 5.5
C. 11
D. 2.25
A. Find the measure of SR.
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A. A
B. B
C. C
D. D
A. 28
B. 30
C. 15
D. 30
B. Find the measure of HFI.
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A. A
B. B
C. C
D. D
A. 7
B. 14
C. 19
D. 25
C. Find the measure of UV.
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Use the Incenter Theorem
A. Find SU if S is the incenter of ΔMNP.
Answer: SU = 6
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Use the Incenter Theorem
B. Find SPU if S is the incenter of ΔMNP.
Answer: mSPU = (62) or 31__12
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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.
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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.