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• inscribed angle
• intercepted arc
Use Inscribed Angles to Find Measures
A. Find mX.
Answer: mX = 43
Use Inscribed Angles to Find Measures
B.
= 2(52) or 104
A. 47
B. 54
C. 94
D. 188
A. Find mC.
A. 47
B. 64
C. 94
D. 96
B.
Use Inscribed Angles to Find Measures
ALGEBRA Find mR.
R S R and S both intercept . mR mS Definition of congruent angles
12x – 13 = 9x + 2 Substitutionx = 5 Simplify.
Answer: So, mR = 12(5) – 13 or 47.
A. 4
B. 25
C. 41
D. 49
ALGEBRA Find mI.
Use Inscribed Angles in Proofs
Write a two-column proof.
Given:
Prove: ΔMNP ΔLOP
1. Given
Proof:Statements Reasons
LO MN2. If minor arcs are congruent, then corresponding chords
are congruent.
Use Inscribed Angles in Proofs
Proof:Statements Reasons
M L 4. Inscribed angles of the same arc are congruent.
MPN OPL 5. Vertical angles are congruent.
ΔMNP ΔLOP 6. AAS Congruence Theorem
3. Definition of intercepted arcM intercepts and
L intercepts .
Write a two-column proof.
Given:
Prove: ΔABE ΔDCE
Select the appropriate reason that goes in the blank to complete the proof below.
1. Given
Proof:Statements Reasons
AB DC 2. If minor arcs are congruent, then corresponding chords are congruent.
Proof:Statements Reasons
D A 4. Inscribed angles of the same arc are congruent.
DEC BEA 5. Vertical angles are congruent.
ΔDCE ΔABE 6. ____________________
3. Definition of intercepted arcD intercepts and
A intercepts .
A. SSS Congruence Theorem
B. AAS Congruence Theorem
C. Definition of congruent triangles
D. Definition of congruent arcs
Find Angle Measures in Inscribed Triangles
ALGEBRA Find mB.
ΔABC is a right triangle because C inscribes a semicircle.
mA + mB + mC = 180 Angle Sum Theorem(x + 4) + (8x – 4) + 90 = 180 Substitution
9x + 90 = 180 Simplify.9x = 90 Subtract 90 from each
side.x = 10 Divide each side by 9.
Answer: So, mB = 8(10) – 4 or 76.
A. 8
B. 16
C. 22
D. 28
ALGEBRA Find mD.
Find Angle Measures
INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT.
Find Angle Measures
Since TSUV is inscribed in a circle, opposite angles are supplementary.
mS + mV = 180 mU + mT = 180 mS + 90 = 180 (14x) + (8x + 4) = 180
mS = 90 22x + 4 = 18022x = 176
x = 8Answer: So, mS = 90 and mT = 8(8) + 4 or 68.
A. 48
B. 36
C. 32
D. 28
INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mN.