Download m∠A = m∠B = 3. m∠C = m∠D = INTERCEPTED ARC Corollary: (1

GEOMETRY
Inscribed Angles
NAME_________________________
DATE __________ Per.___________
Circles
3.
Which arc measure does each inscribed
angle equal?
A
4.
SC is the diameter.
mSC =
R
m∠A =
m∠B =
D
m∠SRC =
S
C
B
C
Semi-Circle
COROLLARY:
m∠C =
m∠D =
An angle inscribed in
a semi-circle is a
_____________ angle.
INTERCEPTED ARC Corollary:
The arc intercepted by a right angle is a
____________-_______________.
If two inscribed angles intercept the same arc,
then the angles are ___________________.
5.
Which angle measure does each arc equal?
D
A
(1/2)
minor arc DU = m∠_____
(1/2) Major arc DQU =
mDU + mDQU = 360°
m∠A+ m∠Q = ______°
U
(1/2)
minor arc AQ =
(1/2) Major arc QDA = m∠_____
Q
mAQ + mQDA = _____°
CYLIC QUADRILATERAL Corollary: m∠_____+ m∠_____ = 180°
Opposite angles in a quadrilateral inscribed in a circle (aka acylic quadrilateral) are _______________.
The angle formed by a secant and tangent lines to a circle is half the measure of its intercepted arc.
Justify each statement with a reason.
1) mASD = 180°
2) mDA = 180°
GIVEN: TN tangent to circle C
3) AD ⊥ TN
PROVE: m∠SAN = mSA ÷ 2;
4) ∠DAT is right
m∠TAS = m∠SDA ÷ 2; & m∠DAT = mDA ÷2
5) m∠DAT = 90°
6) m∠SAD = x° ÷ 2
D
7) mSA + mDS = mDSA
x°
8) mSA + x°= 180°
S
9) mSA = 180° – x°
10) mSA ÷ 2 = 90° – x°÷2
11) m∠DAS + m∠SAN = 90°
C
12) m∠SAN = 90° – m∠DAS
13) m∠SAN = mSA ÷ 2
14) m∠DAT = mDA ÷ 2
15) mADS = mAD + mDS (= 180° + x°)
16) m∠TAS = m∠DAT + m∠SAD
17) m∠TAS = 90° + x°÷2 = mSDA ÷ 2
T
A
N
6.