Page 168 - Math Course 3 (Book 2)

Inscribed Angles

Find m∠3. Find m∠4. MO. 11 - L4b

A. 30 A. 110 Measures of Angles of
B. 80 B. 55
C. 40 C. 125 Inscribed Polygons
D. 10 D. 27.5

THEOREM 11.7
Answer Answer

If the inscribed angle of a triangle intercepts a
semicircle, the angle is a right angle.

Example: ADC is a semicircle, so m∠ABC = 90.

A

Find m∠5.

A. 110 D
B. 55
C. 125
D. 27.5
B C
Answer

Proof with Inscribed Angles
Choose the best reason to complete the following THEOREM 11.8
proof. C E If a quadrilateral is inscribed in a circle, then its
opposite angles are supplementary.
Given: ⊙M; CJ ≅ EH
Prove: ΔCEM ≅ ΔHJM
M Example: Quadrilateral ABCD is inscribed in ⊙P.
∠A and ∠C are supplementary.
∠B and ∠D are supplementary.

J H B
Proof:
Statement Reasons C

1. ⊙M; CJ ≅ EH 1. Given P

2. ∠ECM ≅ ∠JHM 2. ___________

3. ∠CME ≅ ∠HMJ 3. Vertical angles are congruent. A
D
4. CM ≅ HM 4. Radii of a circle are congruent

5. ΔCEM ≅ ΔHJM 5. ASA

A. Alternate Interior Angle Theorem
B. Substitution
C. Definition of ≅ angles
D. Inscribed angles of ≅ arcs are ≅.

Answer

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