Over Lesson 1–4 A.A B.B C.C D.D 5-Minute Check 1 A.V B.P C.Q D.R E.T F.S G.U Name the coordinates…
Over Lesson 10–3 A.A B.B C.C D.D 5-Minute Check 1 80.
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Transcript of Over Lesson 10–3 A.A B.B C.C D.D 5-Minute Check 1 80.
Over Lesson 10–3
A. A
B. B
C. C
D. D
26.8
to the nearest tenth.
• Find measures of inscribed angles.
• Find measures of angles of inscribed polygons.
In this lesson we will:
• inscribed angle—An angle whose vertex lies on a circle and whose sides contain chords of the circle.
• intercepted arc—The arc formed by an inscribed angle.
Use Inscribed Angles to Find Measures
A. Find mX.
Answer: mX = 43
Use Inscribed Angles to Find Measures
B.
= 2(252) or 104
Use Inscribed Angles to Find Measures
ALGEBRA Find mR.
R S R and S both intercept . mR mS Definition of congruent
angles12x – 13 = 9x + 2 Substitution
x = 5 Simplify.Answer: So, mR = 12(5) – 13 or 47.
Use Inscribed Angles in Proofs
Write a two-column proof.
Given:
Prove: ΔMNP ΔLOP
1. Given
Proof:Statements Reasons
LO MN 2. 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 ΔDCESelect 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 .
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.
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.
S + V = 180 S + V = 180 S + 90 = 180 (14x) + (8x + 4) = 180
S = 90 22x + 4 = 18022x = 176
x = 8Answer: So, mS = 90 and mT = 8(8) + 4 or 68.
A. A
B. B
C. C
D. D
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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.
