TODAY IN GEOMETRY… Review: Learning Target : 10.4 You will use inscribed angles of circles Independent practice CH.10 QUIZ - FRIDAY

REVIEW: Graph △𝐴𝐵𝐶. 𝐴 3, 4 𝐵 −1, 5 𝐶 1, −2 Translate the Pre-Image and record the image points. (𝑥, 𝑦)→(𝑥−2, 𝑦+3) 𝐴′ 𝐵′ 𝐶′ 𝑃𝑜𝑖𝑛𝑡 𝐴: 3, 4 → 3−2, 4+3 (3, 4)→(1, 7) 𝑨′(𝟏, 𝟕) 𝑃𝑜𝑖𝑛𝑡 𝐵: −1, 5 → −1−2, 5+3 (−1, 5)→(−3, 8) 𝑩′(−𝟑, 𝟖) 𝑃𝑜𝑖𝑛𝑡 𝐶: 1, −2 → 1−2, −2+3 1, −2 → −1, 1 𝑪′(−𝟏, 𝟏) 𝐴 𝐵 𝐶

REVIEW: Graph △𝐴𝐵𝐶. 𝐴 3, 4 𝐵 −1, 5 𝐶 1, −2 Reflect the pre-image across the y-axis. RULE FOR RELECTION ACROSS Y-AXIS: (𝑥, 𝑦)→(−𝑥, 𝑦) 𝐴′ 𝐵′ 𝐶′ 𝐴 𝐵 𝐶 𝑃𝑜𝑖𝑛𝑡 𝐴: 3, 4 → −3, 4 𝑃𝑜𝑖𝑛𝑡 𝐵: −1, 5 → 1, 5 𝑃𝑜𝑖𝑛𝑡 𝐶: 1, −2 → −1, −2

REVIEW: Graph △𝐴𝐵𝐶. 𝐴 3, 4 𝐵 −1, 5 𝐶 1, −2 Reflect the pre-image across the line 𝑥=1. EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF REFLECTION 𝐴′ 𝐵′ 𝐶′ 𝑃𝑜𝑖𝑛𝑡 𝐴: 7, 1 → −5, 1 𝑃𝑜𝑖𝑛𝑡 𝐵: 3, 2 → −1, 2 𝑃𝑜𝑖𝑛𝑡 𝐶: 5, −5 → −3, −5 𝐴 𝐵 𝐶 𝑥=1

SOME IMPORTANT DEFINITIONS-not on your notes: INSCRIBED ANGLE: An angle whose vertex is on circle. INTERCEPTED ARC: The arc made from an inscribed angle.

INSCRIBED ARC FORMULA: The measure of an inscribed angle is one half the measure of its intercepted arc. Intercepted arc Inscribed arc 𝑥 2𝑥

PRACTICE:

PRACTICE:

Two inscribed angles that intercept the same arc are congruent. 𝐵 Be able to see that these figures are the same! Shared Intercepted arc 𝐴 𝐴 𝐵 𝐶 𝐷 𝐷 𝐶

PRACTICE: 1 2 90° =𝟒𝟓° 2 38° =𝟕𝟔° 𝟕𝟐°

The circle that contains the vertices is a circumscribed circle. A polygon is an inscribed polygon if all of its vertices lie on the circle. The circle that contains the vertices is a circumscribed circle. Circumscribed circle Inscribed triangle Inscribed polygon

A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. 𝐹 𝑚∠𝐷+𝑚∠𝐹=180° 𝐺 𝐸 𝑚∠𝐸+𝑚∠𝐺=180° 𝐷

Opposite angles of an inscribed polygon are supplementary: PRACTICE: Opposite angles of an inscribed polygon are supplementary: a. 𝑦+75°=180° − 75 − 75 𝒚=𝟏𝟎𝟓° 𝑥+80°=180° − 80 − 80 𝒙=𝟏𝟎𝟎° b. 2𝑎+2𝑎=180° 4𝑎=180° 4 4 𝒂=𝟒𝟓 4𝑏+2𝑏=180° 6𝑎=180° 6 6 𝒂=𝟑𝟎

Opposite angles of an inscribed polygon are supplementary: PRACTICE: Opposite angles of an inscribed polygon are supplementary: 6. 8𝑥+10𝑥=180° 18𝑥=180° 18 18 𝒙=𝟏𝟎 5. 𝑦+68°=180° − 68 − 68 𝒚=𝟏𝟏𝟐° 𝑥+82°=180° − 82 − 82 𝒚=𝟗𝟖° 𝑐+2𝑐−6=180° 3c−6=180° + 6 + 6 3𝑐=186 3 3 𝒄=𝟔𝟐

HOMEWORK #4: Pg. 676: 3-16 Pg. 679: 40-46 If finished, work on other assignments: HW #1: Pg. 655: 3-20, 24-26, 30 HW #2: Pg. 661: 3-14, 17, 23 HW #3: Pg. 667: 3-15