Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1...
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Transcript of Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1...
![Page 1: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/1.jpg)
![Page 2: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/2.jpg)
Theorem 12-9:
The measure of an inscribed angles is half
the measure of its intercepted
arc.
mB=1/2mAC
(
B
A
C
![Page 3: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/3.jpg)
Example”
Find the measure of A
A
B
C
D
900
1100
600
1000
mA=1/2mBCD
(mA=1/2(900+600)mA=1/2(1500)mA=750
![Page 4: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/4.jpg)
Example”
Find the measure of D
A
B
C
D
900
1100
600
1000
mD=1/2mABC
(mD=1/2(1000+900)mD=1/2(1900)mD=950
![Page 5: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/5.jpg)
Corollaries #1
Two inscribed angles that intercept the same arc are congruent.
mBmCB
C
![Page 6: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/6.jpg)
Corollaries #2
An angle inscribed in a semicircle is a right angle
mB=900
B
![Page 7: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/7.jpg)
Corollaries #3
The opposite angles of a quadrilateral inscribed in a circle are supplementary.
mA+mC=1800
mB+mD =1800B
D
A
C
![Page 8: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/8.jpg)
Example”
Find the measure of a and b.
a
b0 O320A is inscribed in a semi-circle, a is a right
angle
![Page 9: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/9.jpg)
Example”
Find the measure of a and b.
a
b0 O320a=900
The sum of the angles of a triangle is 1800, the other angle is 1800-900-320=580
580
![Page 10: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/10.jpg)
Example”
Find the measure of a and b.
a
b0 O320a=900
580=1/2b580
2 21160 =b
![Page 11: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/11.jpg)
Theorem 12-10:
The measure of an angle formed by a
tangent and a chord is half the measure of the intercepted arc.
mC=1/2mBDC
(
B
D
C
![Page 12: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/12.jpg)
Example:
RS and TU are diameters
of A. RB is tangent to
A at point R. Find
mBRT and mTRS.
B
R
U
S
A1260
T
![Page 13: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/13.jpg)
mBRT
B
R
U
S
A1260
T
mBRT=1/2m RT
)
mRT=mURT-mUR
) ) )
mRT=1800-1260
)
mRT=540
)
mBRT=1/2(540)mBRT=270
![Page 14: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/14.jpg)
mTRS
B
R
U
S
A1260
T
mBRS=mBRT+mTRS
270
900=270+mTRS
630=mTRS
![Page 15: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/15.jpg)
![Page 16: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/16.jpg)
![Page 17: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/17.jpg)
![Page 18: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/18.jpg)
![Page 19: Theorem 12-9: The measure of an inscribed angles is half the measure of its intercepted arc. m B= 1 / 2 mAC ( B A C.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649edb5503460f94bead18/html5/thumbnails/19.jpg)