Splash Screen

Section 10.4 (part 2) WB Pg. 31 #1-12 1. a = 100° 2. b = 40°   1. a = 100° 2. b = 40° 3. c = 23° 4. d = 82° 5. e = 50° 6. f = 84° 7. g = 50° 8. h = 84° 9. i = 48° 10. a = 35° 11. b = 70° 12. c = 25° 13. d = 70° 14. e = 35° 15. f = 25° 16. g = 50° g  80 42 46 a b i P f c e h d  P d c b a g f e 50 70

A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency. is tangent to at point A. and are also called tangents.

A common tangent is a line, ray, or segment that is tangent to two circles in the same plane. In each figure below, in l is a common tangent of circles F and G.

Identify Common Tangents A. Using the picture on the right, draw the common tangents. If no common tangent exists, state no common tangent. Example 1

Identify Common Tangents B. Using the figure to the right, draw the common tangents. If no common tangent exists, state no common tangent. Example 1

Concept

Identify a Tangent A) Example 2

B) Example 2

Use a Tangent to Find Missing Values Example 3

B) Example 3

Think of the 2 tangents as a party hat! Watch: Think of the 2 tangents as a party hat! The sides of the hat are congruent  Concept

Use Congruent Tangents to Find Measures Example 4

B) Example 4

Circumscribed Polygons A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

Find Measures in Circumscribed Polygons Example 5

B) Example 5

DAY 2: C) XY = 22 YZ = 15 ZW= 16 Find XW. W Y X Z Example 5

DAY 2: Practice Complete WB Pg. 28 #1 and 4 Complete WB Pg. 31 #10-16 (choose any three) Complete WB Pg. 27 #1-6 SKILLS CHECK when 15 minutes are left HW: Anything from 1-3 that is not finished!

End of the Lesson

Mathematical Practices Content Standards G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.C.4 Construct a tangent line from a point outside a given circle to the circle. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. CCSS

Use properties of tangents. You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed polygons. Then/Now

tangent point of tangency common tangent Vocabulary

Five-Minute Check (over Lesson 10–4) CCSS Then/Now New Vocabulary Example 1: Identify Common Tangents Theorem 10.10 Example 2: Identify a Tangent Example 3: Use a Tangent to Find Missing Values Theorem 10.11 Example 4: Use Congruent Tangents to Find Measures Example 5: Real-World Example: Find Measures in Circimscribed Polygons Lesson Menu

Refer to the figure. Find m1. A. 60 B. 55 C. 50 D. 45 5-Minute Check 1

Refer to the figure. Find m2. A. 30 B. 25 C. 20 D. 15 5-Minute Check 2

Refer to the figure. Find m3. A. 35 B. 30 C. 25 D. 20 5-Minute Check 3

Refer to the figure. Find m4. A. 120 B. 100 C. 80 D. 60 5-Minute Check 4

find x if mA = 3x + 9 and mB = 8x – 4. C. 12 D. 13 5-Minute Check 5

The measure of an arc is 95° The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it? A. 47.5° B. 95° C. 190° D. 265° 5-Minute Check 6