• 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.