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Five-Minute Check (over Lesson 10–3)
Then/Now
New Vocabulary
Theorem 10.6: Inscribed Angle Theorem
Proof: Inscribed Angle Theorem (Case 1)
Example 1: Use Inscribed Angles to Find Measures
Theorem 10.7
Example 2: Use Inscribed Angles to Find Measures
Example 3: Use Inscribed Angles in Proofs
Theorem 10.8
Example 4: Find Angle Measures in Inscribed Triangles
Theorem 10.9
Example 5: Real-World Example: Find Angle Measures
Over Lesson 10–3
A. 60
B. 70
C. 80
D. 90
Over Lesson 10–3
A. 40
B. 45
C. 50
D. 55
Over Lesson 10–3
A. 40
B. 45
C. 50
D. 55
Over Lesson 10–3
A. 40
B. 30
C. 25
D. 22.5
Over Lesson 10–3
A. 24.6
B. 26.8
C. 28.4
D. 30.2
Over Lesson 10–3
A.
B.
C.
D.
You found measures of interior angles of polygons. (Lesson 6–1)
• Find measures of inscribed angles.
• Find measures of angles of inscribed polygons.
• 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.
