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

2. 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

3. 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

4. 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

5. 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.

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

7. PRACTICE:

8. PRACTICE:

9. 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

10. PRACTICE:
° =𝟒𝟓°
2 38° =𝟕𝟔°
𝟕𝟐°

11. 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

12. 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

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

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

15. 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